Objective 2. TEKS A.2.A Review. line. Name Date TAKS

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1 Objective TEKS A..A Review A..A Identif and sketch the general forms of linear ( ) and quadratic ( ) parent functions. A linear function is one whose graph is a straight line. Linear functions can be written in the form m b. The graph of a quadratic function is U-shaped. Quadratic functions can be written in the form a b c. Parent function Graph TEKS A..A Review Shape Line Parabola EXAMPLE What is the equation of the parent function of the graph shown here? YOU DO IT The graph is a parabola so the parent function is. What is the equation of the parent function of the graph shown here? The graph is a. line, so the parent function is Copright b McDougal Littell, a division of Houghton Mifflin Compan. TEKS A..A Review Objectives Review and Practice Grade (Eit Level) Test

2 Objective TEKS A..A Practice. Which is the parent function of the graph shown here?. Which is the parent function of the graph shown here? A Ï } B C D. Which is the parent function of the graph shown here? F Ï } G H J. The equation is the parent function of which of these graphs? A TEKS A..A Practice Copright b McDougal Littell, a division of Houghton Mifflin Compan. F Ï } G H J. Which is the parent function of the graph shown here? A Ï } B C D B C D h A..A When ou finish this page, ou can check off a bo on our TEKS Tracker, page. Objectives Review and Practice Grade (Eit Level) Test TEKS A..A Practice

3 Objective TEKS A..B Review A..B Identif mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete. The domain of a function is the set of all the values for the independent variable, often denoted as. The range of a function is the set of all the values for the dependent variable, often denoted as. On a graph, the domain is the set of -coordinates of the points on the graph and the range is the set of -coordinates of the points on the graph. EXAMPLE What is the domain of the function shown in this graph? What is the range? TEKS A..B Review The -coordinate of the point farthest to the left in the graph is and the -coordinate of the point farthest to the right is, so the domain is. The -coordinate of the lowest point in the graph is and the -coordinate of the highest point in the graph is, so the range is. YOU DO IT. What is the domain of the function shown in this graph? The -coordinate of the point farthest to the left on the graph is. The -coordinate of the point farthest to the right is point (, ) is shown as an open circle, its -coordinate is domain. The domain is <.. What is the range of the function shown in the graph above? The -coordinate of the lowest point in the graph is the highest point is, but since the part of the. The -coordinate of, but since the point (, ) is shown as an open circle, its -coordinate is not part of the range. The range is <. not Copright b McDougal Littell, a division of Houghton Mifflin Compan. TEKS A..B Review Objectives Review and Practice Grade (Eit Level) Test

4 Objective TEKS A..B Practice. What is the domain of the function shown in this graph?. The function gives the total cost of paperback books. What is a reasonable domain for this function? F {,,,,...} G {...,,,,,,...} H J All real numbers Copright b McDougal Littell, a division of Houghton Mifflin Compan. A < < B C < D. What is the range of the function shown in the graph for question? F < < G H < J. The corners of a square piece of cardboard are cut out and the sides folded up to form an open bo as shown in the figure below. in. in. The area of the bottom of the bo is given b the function A ( ). What is a reasonable domain for this function? A < B < < C < < D < <. Rosie threw a ball into the air with an initial velocit of feet per second. The height of the ball after t seconds is given b the function t t. The graph of height versus time is shown. What is a reasonable range for this function? Height (ft) t Time (sec) A All real numbers B C D. A cellular phone service compan charges cents for each minute or part of a minute of airtime. If the total charge is a function of the number of minutes that Cora uses her phone, what is the range of this function? F {,,,,,...} G H {,,,,...} J TEKS A..B Practice h A..B When ou finish this page, ou can check off a bo on our TEKS Tracker, page. Objectives Review and Practice Grade (Eit Level) Test TEKS A..B Practice

5 Objective TEKS A..C Review A..C Interpret situations in terms of given graphs or create situations that fit given graphs. You can interpret situations in terms of a given graph b looking at the scales used on the aes of the graph, considering the domain and range of the graph, and looking for changes in the data. Does it increase, decrease, or sta constant? The graph should reflect these changes. Also, make sure the correct quantities are the ones shown on the aes. EXAMPLE Marlene has an antique vase. Draw a graph that shows the value of her vase as it increases over time until one da when she dropped the vase and it shattered. What was the value of the vase when she dropped it? TEKS A..C Review Value (dollars) Time (r) The segment goes up indicating the value is increasing. The quantities on the aes are time and value. At the time she dropped the vase, the value immediatel drops to $. The vase was worth about $ when she broke it. YOU DO IT The graph shows the altitude of an airplane as a function of time as it takes off, flies at a constant altitude for awhile and then slowl descends. What is the altitude of the plane hours after takeoff? Altitude (thousands of feet) Time (h) When the airplane takes off, its altitude is feet so the graph starts at the point (, ). When the plane reaches its maimum altitude and levels off, the graph becomes horizontal. As the plane descends, its altitude decreases. Two hours after takeoff, the altitude of the plane was, feet. Copright b McDougal Littell, a division of Houghton Mifflin Compan. TEKS A..C Review Objectives Review and Practice Grade (Eit Level) Test

6 Objective TEKS A..C Practice. The graph shows the wind speed as a storm develops. To the nearest whole number, what was the average increase per minute between and minutes?. Which graph models the depth of water in a sink as it increases inches per minute? A Wind speed (mi/h) Time (min) Record our answer and fill in the bubbles in the grid below. Be sure to use the correct place value.. B C Depth (in.) Depth (in.) Time (min) Time (min) TEKS A..C Practice Copright b McDougal Littell, a division of Houghton Mifflin Compan.. The graph shows the value of an initial $ investment over time. How much did the value increase each ear? Value(dolars) D Depth (in.) Depth (in.) Time (min) Time (min) Years F $ G $ H $ J $ Objectives Review and Practice Grade (Eit Level) Test h A..C When ou finish this page, ou can check off a bo on our TEKS Tracker, page. TEKS A..C Practice

7 Objective TEKS A..D Review A..D Collect and organize data, make and interpret scatterplots (including recognizing positive, negative, or no correlation for data approimating linear situations), and model, predict, and make decisions and critical judgments in problem situations. To predict values using a scatterplot, look for a pattern in the data. Draw a line through the data that represents the trend of the values and use points on this line for our predictions. If the line slopes up to the right, the correlation is positive. If the line slopes down to the right, the correlation is negative. If there is no pattern to the data and ou cannot draw a line to show the trend, there is no correlation. TEKS A..D Review EXAMPLE The graph shows the population of a town at four times from. Use the graph to predict the population in the ear. Population (thousands) The population has increased b about people during these ears, or about people per ear. Since is ears after, it will increase about. The population of the town will be about, people in the ear. YOU DO IT Year The table shows the number of participants in water aerobics at a fitness center at three times from. If this trend continues, how man participants would ou epect for water aerobics in the ear? Year Participants From to, the number of participants increased b or an average of people per ear. From to, the number increased b or an average of. } people per ear. Therefore, in, which is ears after, if ou epect an average increase of about people per ear, the total increase will be about people. So, the number of epected participants in will be about people. Copright b McDougal Littell, a division of Houghton Mifflin Compan. TEKS A..D Review Objectives Review and Practice Grade (Eit Level) Test

8 Objective TEKS A..D Practice Copright b McDougal Littell, a division of Houghton Mifflin Compan.. The table gives the number of stories and height of several tall buildings. Building Stories Height (ft) Sears Tower Empire State Building Chrsler Building JP Morgan Chase Tower One Libert Place Based on the values in the table, which is a reasonable estimate for the height of the Wells Fargo Plaza building in Houston, which has stories? A B C D About ft About ft About ft About ft. The table gives the prices for packages of -inch b -inch photo paper, with a different number of sheets in the package. Sheets Cost $. $. $. Which is a reasonable estimate of the price for a package containing sheets of -inch b -inch photo paper? F $. G $. H $. J $.. The following table shows the approimate enrollment at Teas communit colleges in the ears,, and. If the trend shown in the data continues, how man students would ou epect to be enrolled in Teas communit colleges in the ear? A B C D Year Enrollment,,, About, students About, students About, students About, students. Bill had lunches at his favorite restaurant three times this ear with different numbers of friends. The total cost of the meals each time is shown in this table. Lunches Cost $. $. $. Based on this table, if Bill and friends eat at this restaurant before prom, about what will be the epected total cost? F About $ G About $ H About $ J About $ TEKS A..D Practice h A..D When ou finish this page, ou can check off a bo on our TEKS Tracker, page. Objectives Review and Practice Grade (Eit Level) Test TEKS A..D Practice

9 Objective TEKS A..A Review A..A Use smbols to represent unknowns and variables. You can use variables to represent unknown quantities in epressions, equations, or inequalities. If ou are given a value for the variable, substitute it into the equation or inequalit and solve for the remaining variable. EXAMPLE If represents the length of a rectangle and represents the width, write a function to represent the perimeter P of the rectangle. Then write a function to represent the area A of the rectangle. Perimeter length width Formula for the perimeter of a rectangle P Substitute the given epressions. TEKS A..A Review YOU DO IT P Area length width A A Simplif. Formula for the area of a rectangle Substitute the given epressions. Simplif.. If the radius of a circle is represented b, write a function f() to represent the circumference of the circle. The formula for the circumference of a circle is C. Substituting f() for C and for r gives. Simplifing this result gives f().. Use the function from Eercise. When meters, what is the circumference of the circle? Round our answer to the nearest tenth. f() p( ) Substitute for.. p Simplif. meters Use. for p and round to the nearest tenth.. Tomas wants to find a function that will give the distance from the point at (, ) to an point on the line. Write a function that gives the distance f() as a function of onl. Ever point on the line has the form (, ). The distance formula is d. Using the two points (, ) and (, gives the function: f() Ï }}}} ( ) ( ) Ï }}} ( ) ( ) f () () r Ï }} ( ) ( ) ), the distance formula Copright b McDougal Littell, a division of Houghton Mifflin Compan. TEKS A..A Review Objectives Review and Practice Grade (Eit Level) Test

10 Objective TEKS A..A Practice. Force equals mass times acceleration. If m represents mass and a represents acceleration, which function f represents force? A f ma B f m a C f m a D f m } a. The height of a clindrical can is twice its radius, as shown in this figure. r r. The figure below is a sketch of a rectangular tablecloth. b If b is the width and a represents the length, which function d gives the length of the diagonal? F d a b G d } ab a Which function gives the volume V(r) of the can as a function of the radius r? F V(r) pr h G V(r) pr H V(r) pr J V(r) pr. A line has slope c and -intercept d. Which equation gives the -coordinate of a point on the line as a function of the -coordinate of the point? A c d B c d C cd D d c TEKS A..A Practice Copright b McDougal Littell, a division of Houghton Mifflin Compan. H d Ï } ab J d Ï } a b. Donita is building a ramp for her to cars. A side view of the ramp is shown below. h Which function gives the length of the shorter leg f(h) of the triangle as a function of the hpotenuse h? A f(h) h B f(h) h C f(h) } h D f(h) Ï} } h. Noah rides his biccle at a constant speed of m miles per hour for a distance of miles. Which function f() gives the time he rides as a function of the distance? F f() } m G f() m H f() m J f() } m. Which function gives the distance from the point at (, ) to a point on the line as a function of just? A f() ( )( ) B f() } C f() D f() Ï }} ( ) ( ) Objectives Review and Practice Grade (Eit Level) Test h A..A When ou finish this page, ou can check off a bo on our TEKS Tracker, page. TEKS A..A Practice

11 Objective TEKS A..B Review A..B Look for patterns and represent generalizations algebraicall. When first eamining a real-world situation, tr to use numbers to represent it. List the numbers to help ou find a pattern. Use the pattern to write an algebraic epression for the situation. Then check each number in our list to be sure it satisfies the epression. EXAMPLE A contractor has just started laing tile in a new house. The figures show the tile pieces as he put them down. TEKS A..B Review YOU DO IT Write a rule to epress the pattern of the numbers of black triangles in each figure. List the number of black triangles:,,. The numbers increase b, so the rule must contain the term n, where n is the figure number. When ou substitute for n, the result needs to be, so the rule must be n. Check for n and n : () and (). The rule is correct. Mark is putting photos in a photo album. Some photos are vertical and others are horizontal. The figures show the photos in the order he placed them in the album. Step : Step : Step : Write a formula to epress the difference between the number of horizontal photos and the number of vertical photos at each step n. Begin b completing this table. Step Horizontal photos Vertical photos Difference The difference decreases b for each successive step, so the rule needs to contain the term n, where n is the step number. When n, the result needs to be, so the rule must be n. Copright b McDougal Littell, a division of Houghton Mifflin Compan. TEKS A..B Review Objectives Review and Practice Grade (Eit Level) Test

12 Objective TEKS A..B Practice Copright b McDougal Littell, a division of Houghton Mifflin Compan.. The pattern of dots shown below continues after step, with more dots added at successive each step. Step Step Step Step Which rule can be used to determine the number of dots that would appear in the nth step? A n (n ) } B n C n D n. A store displa is created b arranging rows of soup cans in the shape of a triangle. There are cans in the first row. In the second row there are cans. The third row contains cans, and so forth. Which rule gives the number of cans in the nth row, where n? F n G n H n J n. The pattern of dots shown below continues after step, with more dots added at each successive step. Step Step Step Which rule can be used to determine the number of dots that would appear in the nth step? A n B n C n D n. The seats in an auditorium are arranged so there are seats in the front row, seats in the second row, seats in the third row, and so forth. Which rule could be used to determine the number of seats in the rth row, where r? F r G r H r J r. There was one cracked cement square in a sidewalk as indicated b the shaded square. A construction compan is adding squares to the sidewalk in the quantities shown in the figure below. Step Step Step Which rule will give the ratio of shaded squares to unshaded squares at the nth step of the figure? A } n B } n C } n D n. Tim has started a weightlifting routine. Each week he increases the number of repetitions as follows:,,,.... Which epression gives the number of repetitions Tim will do in the nth week? F n G n H n J n TEKS A..B Practice h A..B When ou finish this page, ou can check off a bo on our TEKS Tracker, page. Objectives Review and Practice Grade (Eit Level) Test TEKS A..B Practice

13 Objective TEKS A..A Review A..A Find specific function values, simplif polnomial epressions, transform and solve equations, and factor as necessar in problem situations. To find function values, substitute the value of the independent variable into the function and solve for the dependent variable. To simplif polnomial epressions, first rewrite the epression so it is just the sum and/or difference of monomial terms. Then combine all like terms. To solve equations, add to or subtract from both sides of the equation so ou get the variable terms on one side and the constant terms on the other side. Combine the like terms. Then divide both sides b the coefficient of the variable. TEKS A..A Review EXAMPLE Manuel is building a deck around his pool as shown in the diagram below. Write an epression for the area of the deck. Deck Pool YOU DO IT First, find an epression for the area of the entire figure (the deck and the pool) and another epression for the area of just the pool. The area of the deck can then be found b subtracting the area of the pool from the area of the entire figure. ( )( ) () () () () Area of deck and pool ()() Area of pool ( ) Area of deck The function f(t) (t ) gives the height in feet of a ball t seconds after it is thrown into the air. Find the height of the ball after seconds. f() ( ) Substitute for t. ( ) The ball will be feet above the ground after seconds. Copright b McDougal Littell, a division of Houghton Mifflin Compan. TEKS A..A Review Objectives Review and Practice Grade (Eit Level) Test

14 Objective TEKS A..A Practice. What is the solution of? Record our answer and fill in the bubbles in the grid below. Be sure to use the correct place value.. Corbin has a triangular piece of stained glass as shown below. What is its perimeter?.. A car rental compan charges $ per da with unlimited mileage. Another car rental compan charges $ per da plus cents per mile for the same vehicle class. To determine how man miles Traci must drive her rental car in order for the second plan to cost the same as the first plan, she has written the equation.. What is the solution of her equation? A B C D. Erica is painting a warning cone to use to block her drivewa while it is being repaired. The surface area of the cone is given b the function S(r) p r pr, where r is its radius. Erica s cone has a radius of inches. What is its surface area, S()? Use. for p. TEKS A..A Practice ( ) in. ( ) in. Record our answer and fill in the bubbles in the grid below. Be sure to use the correct place value. Copright b McDougal Littell, a division of Houghton Mifflin Compan. ( ) in. F ( ) in. G ( ) in. H ( ) in. J in.. Which epression can be factored as the product ( )( )? A B C D. Alisa was working to determine how man terms of the sequence,,,... are needed to get a sum of. She has written the equation n n and needs to find its solution. What are the factors of the epression n n? F (n )(n ) G (n )(n ).. The function f() gives the amount of mone Frank has in his pocket when he has $ bills and seven $ bills. What is f()? A B C D H (n )(n ) J (n )(n ) h A..A When ou finish this page, ou can check off a bo on our TEKS Tracker, page. Objectives Review and Practice Grade (Eit Level) Test TEKS A..A Practice

15 Objective TEKS A..B Review A..B Use the commutative, associative, and distributive properties to simplif algebraic epressions. In the following properties, the variables a, b, and c are all real numbers. Commutative Propert of Addition a b b a Commutative Propert of Multiplication ab ba Associative Propert of Addition a (b c) (a b) c Associative Propert of Multiplication a(bc) (ab)c TEKS A..B Review EXAMPLE YOU DO IT Use the commutative, associative, and distributive properties to simplif the epression ( ) ( )( ). Separate the work into parts. First, simplif the epression ( ) and then simplif the epression ( )( ). Finall, use this work to write the simplified form of the entire epression. ( ) ( ) Commutative Propert of Multiplication () () Distributive Propert Simplif. ( )( ) ( )() ( )() Distributive Propert ( ) ( ) Commutative Propert of Multiplication () () () () Distributive Propert Simplif. Combine like terms. ( ) ( ) Simplif. Use the commutative, associative, and distributive properties to simplif the epression } ( ) ( ). First, simplif just } ( ). Then work to write the simplified form of the entire epression. } ( ) ( ) ( ) Copright b McDougal Littell, a division of Houghton Mifflin Compan. TEKS A..B Review Objectives Review and Practice Grade (Eit Level) Test

16 Objective TEKS A..B Practice. Which epression is equivalent to (n )(n) (n )(n )? A n n n B n n. A dog breeder has ( ) Shetland sheepdogs and ( ) collies. Half of the collies and two-thirds of the sheepdogs are blue merles. Which epression gives the total number of blue merles that the breeder has? C n n A D n n B.. Which epression is equivalent to } (a b) } (a b)? C D Copright b McDougal Littell, a division of Houghton Mifflin Compan. F G H J a b a b a b a b. If ( ) bos go on a picnic and each brings ( ) sandwiches, which epression gives the total number of sandwiches? A B C D. A stop sign has the shape of a regular octagon. What is the perimeter of the stop sign shown here? F G ( z) in. ( z) in. STOP ( z) in.. What is the area of the triangular pendant shown in this figure? ( ) cm F ( ) cm ( ) cm G ( ) cm H (..) cm J ( ) cm. What is the area of this semicircular countertop? ( ) ft A p(. ) ft B p( ) ft C p(. ) ft D p( ) ft TEKS A..B Practice H J ( z ) in. ( z) in. h A..B When ou finish this page, ou can check off a bo on our TEKS Tracker, page. Objectives Review and Practice Grade (Eit Level) Test TEKS A..B Practice

17 Objective Mied Review Mied Review. The function f() gives Ralph s age in terms of his sister Cara s age. If Cara is, how old is Ralph? (A..A) A ears old B ears old C ears old D ears old. Which epression is equivalent to ( )? (A..B) F G H J. The table shows the prices of various sized memor cards. Based on the table, what would ou epect the price of a gigabite ( Mb) memor card to be? (A..D) Size (Mb) Price $ $ $. The radius of a ball used on the plaground is a inches. Which epression gives the volume of the ball? (A..A) F pa in. G pa in. H pa in. J pa in.. Glenn deposited $ into a savings account on his eighth birthda. On his ninth birthda he deposited $ and on his tenth birthda he deposited $ into the account. If he continues this pattern, which epression gives the amount that Glenn will deposit into the account on his nth birthda? (A..B) A n B n C n D n. Which is the parent function of the graph shown here? (A..A) A $ B $ C $ D $. What is the range of the function shown in this graph? (A..B) F G > H J >. Fift-eight is more than times the number of seahorses at an aquarium. Solve the equation. How man seahorses are at the aquarium? (A..A) A seahorses B seahorses C seahorses D seahorses F G H J Ï }. The graph shows the amount of gasoline in a lawnmower as a function of time. How much gasoline does the mower use per hour? (A..C) Gasoline (gal).. h When ou finish this page, ou can check off a bo on our TEKS Tracker, page. Time (h) A gal B gal C gal D. gal Copright b McDougal Littell, a division of Houghton Mifflin Compan. Mied Review Objectives Review and Practice Grade (Eit Level) Test