Semester Eam Review Two-Year Algebra A Semester Eam Review 05 06 MCPS Page
Semester Eam Review Eam Formulas General Eponential Equation: y ab Eponential Growth: A t A r 0 t Eponential Decay: A t A r Continuous Growth: A t Ae 0 Continuous Decay: A t Ae rt 0 0 t Compound Interest (n compoundings per year): rt F t F t P Pe Compound Interest (continuous compounding): rt r n nt log N p p b if and only if b N The average rate of change for a function f on the interval ab, : f b f a b a MCPS Page
Semester Eam Review Unit, Topic. Let f and g be functions that are inverses of each other. Complete the following statements. a. If the point ab, is on the graph of f, then the point is on the graph of g. b. If f 7, then g 7. c. The graphs of f and g are symmetric with respect to the line. d. The range of f is the same as the of g. e. The domain of f is the same as the of g.. Let f and g be functions that are inverses of each other.. a. Give an numerical eample showing why if f, then g b. Give a numerical eample showing why if f, then g.. Let f and g be functions that are inverses of each other. a. If f, then g. b. If f 9, then g. c. If f 7, then g. MCPS Page
Semester Eam Review 4. For each graph below, sketch the inverse function on the graph to its right. a. b. MCPS Page 4
Semester Eam Review 5. Jill sells lemonade. The profit, p, in dollars is a function of the number of glasses of lemonade, g, that she sells. The function that represents this relationship is p g g. 8 a. Write a function that will represent the number of glasses that she will need to sell to earn a profit of p dollars. b. If Jill made a profit of $, how many glasses did she sell? 6. On a national test, a student receives a score based on the number of correct items. The score, s, in points is a function of the number of correct items c. The function that s c c represents this relationship is 00.5 a. Write a function that will give the number of correct items that it will take to receive a score of s. b. A student received a score of 5. How many items did the student get correct? MCPS Page 5
Semester Eam Review Unit, Topic 7. Write the following epression as a radical. a. 5 b. y c. z 8. Determine the eponent that goes into the bo. a. b. 5 4 c. 6 8 d. 6 e. 6 9. Compute. a. 8 b. 5 c. 8 0. Sally solves the radical equation 5 and obtains the solution 5. Is this solution etraneous? Justify your answer.. Giacomo solves the radical equation 4 and obtains the solutions and 4. Determine if either of the solutions are etraneous.. Johnny solves the radical equation and obtains the solution 8. Is this solution etraneous? Justify your answer. MCPS Page 6
Semester Eam Review. Sketch the equations below. a. y b. y c. y d. y 4. Let f 7. a. What is the domain of f? b. What is the range of f? c. On what interval is the function increasing? MCPS Page 7
Semester Eam Review 5. Solve the equation 5 0 6. A bike rider sees a deer crossing the street and puts on the brakes. The distance that he D s travels, in feet, can be modeled by the function 0 5 s, where s is the speed of the bike in miles per hour. If the bike travels a distance of 58 feet, what was his speed? 7. The population, P, of a town can be modeled by the function where is the year. In what year was the population 0,000? P 60, 000 970, MCPS Page 8
Semester Eam Review Unit, Topic 8. There are four functions represented by tables below. They are either eponential or logarithmic. For each table, write a function equation. a. f b. g c. h d. m f g h m 0 5 0 8 5 0 4 5 00 9 65 4 0,000 7 4 5 5 0,000 4 8 5 4 565 6 4 00,000 5 9. For each equation in column, choose the interval in which the solution lies from column. Column Column a. log8 is between 0 and b. 0 is between and c. log 0 is between and d. is between 4 and 5 5 6 0. Write the logarithmic equation that is equivalent to each eponential equation a. 4 6 b. 0 000 c. 0 e. Write the eponential equation that is equivalent to each logarithmic equation. a. log 00 b. ln e c. log9 8 MCPS Page 9
Semester Eam Review. Does each function below represent eponential growth or decay? a. f b. g c. h 5. Write an eponential function in terms of time t (t in years) for each situation. a. There are 00 bacteria at time 0. The bacteria has a continuous growth rate of 70% per year. b. The population of a town is currently 000. The population is growing at an annual rate of % per year. c. Jack puts $500 into a savings account. It earns interest at a nominal annual rate of 6% per year, compounded monthly. d. The number of deer in a forest is decreasing at an annual rate of 8%. There are currently 700 deer in the forest. e. The number of gnats in a swamp decreases at a continuous decay rate of % per year. There are currently 4 billion gnats in the swamp. MCPS Page 0
Semester Eam Review 4. Look at the functions and their graphs below. f g log 0 p ln h Several properties are listed below. For each property, write the function(s) that have this property. You may use f, g, h, or p as your answers. a. The graph of the function has a horizontal asymptote of y 0. b. The function has a range of all real numbers. c. The function is increasing on its entire domain. d. The graph of the function has a y-intercept at the point 0,. e. The domain of the function is the positive real numbers. f. The graph of the function has a vertical asymptote of 0. g. The function has a domain of all real numbers. h. The function is decreasing on its entire domain. i. The graph of the function has an -intercept at the point, 0. j. The range of the function is the positive real numbers. MCPS Page
Semester Eam Review 5. Each function below is a transformation of the function f e. After each given transformation, write the function rule. a. The graph of function g is the graph of f e translated one unit to the right. g b. The asymptote of the graph of function h has the equation y 4. h c. The graph of function p is the graph of f e reflected across the -ais. p d. The graph of function s is the graph of f e reflected across the y-ais. s 6. Each function below is a transformation of the function transformation, write the function rule. a. The graph of function g is the graph of left. g f log. After each given f log translated two units to the b. The asymptote of the graph of function h has the equation. h c. The graph of function p is the graph of p d. The graph of function s is the graph of s f log reflected across the -ais. f log reflected across the y-ais. 7. Evaluate the following logarithms a. log 9 b. log 4 c. log0000 d. ln 6 e e. log6 f. ln e g. log4 8 = h. log00 0 = MCPS Page
Semester Eam Review 8. Solve each equation. Show the work that leads to your solution. Your answer must be eact or accurate to three places after the decimal point. a. 70 56 b. 8t e 000 9. Jack puts $500 in the bank at a nominal rate of interest of % a year. a. If the interest is compounded monthly ( times a year), how much money will Jack have after 5 years. Round your answer to the nearest cent. b. If the interest is compounded continuously, how much money will Jack have at the end of 5 years? Round your answer to the nearest cent. MCPS Page
Semester Eam Review 0. A house had a value of $00,000 at the beginning of 05. Its value increases at the rate of 0% per year. a. Write a function for the value Vt of the house after t years. V t b. What is the value of the house at the beginning of 09t 4? c. What is the average rate of change of the value of the house from the beginning of 0 t 4. Be sure to include the units in your 05 t to the beginning of 09 answer.. A boat has a value of $,000,000 on January, 05. Its value decreases at a rate of 0% per year. a. Write a function for the value Vt of the boat after t years. V t b. What is the value of the boat at the beginning of 00 t 5? c. What is the average rate of change of the value of the house from the beginning of 0 t 5. Be sure to include the units in your answer. 05 t to the beginning of 00 MCPS Page 4