5 1 Worksheet MATCHING: For # 1 4, match each graph to its equation. Not all equations will be used. 1) 2) 3) 4)

Transcription

1 Algebra 1 Name: Per: 5 1 Worksheet MATCHING: For # 1 4, match each graph to its equation. Not all equations will be used. 1) 2) 3) 4) A) yy = xx 3 B) yy = xx + 3 C) yy = 1 2 xx 3 D) yy = xx 3 E) yy = 2 xx F) yy = xx + 3 For # 5 16, (evens) sketch each function, (odds) identify the vertex, find the domain and range, and describe the transformation from the parent function. 5) yy = 1 3 xx 2 6 6) 7) yy = xx + 3 8) 9) yy = 2 xx ) 11) yy = 3 xx 5 12) 13) yy = xx ) 15) yy = 2 xx ) 3

2 17) Write an absolute value equation that is vertically stretched by a factor of 5 and shifted up 3 and left 2 from the parent function yy = xx. 18) Which statement below is true for the graph shown? A) The range is all real numbers. B) The range is y > 3. C) The range is y < 3. D) The range is y < ) Which equation below has a range of y > 5? Hint: draw a sketch of each! A) yy = xx 5 B) yy = xx C) yy = xx + 5 D) yy = xx ) Which of the following statements is not true about the function yy = xx 5 + 2? Hint: draw a sketch! A) The function is a V-shaped graph. B) The function opens downward. C) The graph is translated left 5 units D) The vertex is at (5, 2). from the parent function. 21) Translate the graph of ff(xx) = xx three units to the right and two units up. Write the function after the translation. A graph is provided if needed. 22) Jenni travels by boat to visit her friend. The graph shows the distance in miles that Jenni is away from her friend s location. At what time(s) is Jenni 15 miles away from her friend? BONUS: The equation yy = xx is shifted up 1 unit, left 5 units, and is then reflected over the x-axis. What is the equation of the new graph?

3 Algebra Worksheet Name: Per: Graph the following piecewise functions on the coordinate plane provided iiii xx 11 1) gg(xx) = iiii xx > iiii xx < 22 2) hh(xx) = iiii xx iiii xx 11 3) yy = iiii xx > 11 4) f(x) = xx + 22 iiii xx < iiii xx 33 xx + 22 iiii xx < 00 5) ff(xx) = xx + 33 iiii xx 00 6) ff(xx) = 22 iiii xx iiii xx > 22

4 iiii xx 11 7) gg(xx) = iiii xx > iiii xx < 22 8) hh(xx) = iiii xx 22 10) Which piecewise function is represented by the graph? 33, xx 22 A. ff(xx) = xx 22, xx > 22 33, xx 22 B. ff(xx) = xx 22, xx < 22 33, xx 22 C. ff(xx) = xx + 22, xx > 22 33, xx 22 D. ff(xx) = xx + 22, xx > 22 Solve: 11) 27 = 3cc 3(6 2cc) 12) 8 + 4mm = 9mm 7 13) Given ff = cccc 2, ff = 650, aaaaaa dd = 10. What is the value of c? A. 10 B. 65 C. 6.5 D ) Reflect the graph of ff(xx) = xx in x-axis, vertically compress it by a factor of ½, and translate the function one unit up. What is the equation for the new function? 15) Translate the graph of ff(xx) = xx three units up and two units to the right. What is the equation for the new function? 16) Given the equation yy = xx 1, what is the domain and range of the function? Hint: draw a sketch! 17) Graph: yy = 2 xx 3 + 5

5 Algebra Worksheet Name: Per: For #1 2, Graph each piecewise function. 1) ff(xx) = xx 3, iiii xx < 3 xx + 3, iiii xx 3 2xx 3, iiii xx < 1 2) ff(xx) = 2xx + 1, iiii xx 1 3) Write the absolute value function for #1: 4) Write the absolute value function for #1: 5) Which absolute value function is equivalent to the function: yy = a) yy = xx b) yy = xx c) yy = xx d) yy = xx xx + 6, xx < 2 xx + 2, xx 2 6) Graph the function ff(xx) = 2 xx 1 on the graph to right: 7) Which of the following is the correct piecewise function to represent #6? 2xx 2 if xx < 0 2xx + 2 if xx < 0 A) yy = B) yy = 2xx + 2 if xx 0 2xx 2 if xx 0 2xx 2 if xx < 1 C) yy = 2xx + 2 if xx 1 D) yy = 2xx + 2 if xx < 1 2xx 2 if xx 1

6 For #7 8: Graph the following piecewise functions on the coordinate plane provided , iiii xx 22 7) gg(xx) = xx + 22, iiii xx > 22 44, 8) hh(xx) = 11 xx, 33 iiii xx < 33 iiii xx 33 For #9 13, solve the equations: 9) xx 3 = 7 10) 2xx 3 = 9 11) 3 3xx 1 3 = 21 12) 3xx (5xx + 2) = 4 2xx 13) 8(2xx 3) 11xx = xx 7 For #14 15: Solve and graph each solution. 14) 4aa 3 > 2aa ) 3 < 5xx 2 13

7 Algebra Worksheet Name: Per: For #1 2, List the properties used for each step to solve for xx. Choices: Addition Property of Equality, Subtraction Property of Equality, Multiplication Property of Equality, Division Property of Equality, Distributive Property, Associative Property, Commutative Property 1) Solution Property used 2xx + 1 Given equation + 1 = 9 3 2xx + 1 = 8 3 2) 2xx + 1 = 24 2xx = 23 xx = 23 2 Solution Property used 17 + (3 + 2xx) = 4(xx 1) Given equation 17 + (3 + 2xx) = 4xx + 4 (17 + 3) + 2xx = 4xx xx = 4xx + 4 Combine like terms xx = 4 6xx = 1 6 xx = 8 3 For #3 4, graph each function. 3) yy = 1 3 xx 5 4) yy = 5, iiii xx < 0 2xx + 3, iiii xx 0 D: R: Transformations: 5) Write the equation of the graph shown. 6) What is the range of ff(xx) = 3 xx 2 + 1? A) yy 1 B) yy 1 C) yy 2 D) yy 2

8 Explicit Formula: ff(nn) = ff(1) + (nn 1)dd Recursive Formula: ff(1) =? ; ff(nn) = ff(nn 1) + dd 7) Amanda starts off with $530 in her savings account, and she puts in $60 into her savings account each month. Which formula below represents this situation after nn months? A) ff(nn) = nn B) ff(nn) = nn C) ff(nn) = nn D) ff(nn) = nn 8) Write the recursive formula for the arithmetic sequence: 55, 44, 33, 22, xx + 3, iiii xx < 3 For #9 10: ff(xx) can be expressed as an absolute value function. ff(xx) = xx 3, iiii xx 3 9) Graph ff(xx). 10) Write the absolute value function that models the graph from #9. 11) Which of the following formulas below correctly describe the sequence? Choose all that apply. 40, 38, 36, 34, 32, A) aa nn = 40 2nn E) ff(nn) = 42 2nn I) ff(1) = 42; ff(nn) = ff(nn 1) 2 B) aa nn = 42 2nn F) ff(nn) = nn J) aa 1 = 40; aa nn = aa nn 1 2 C) aa nn = nn G) ff(1) = 40; ff(nn) = ff(nn 1) 2 K) aa 1 = 42; aa nn = aa nn 1 2 D) ff(nn) = 40 2nn H) ff(1) = 2; ff(nn) = ff(nn 1) ) Which sequence below matches the explicit formula? ff(nn) = 5 + 6nn A) 5, 1, 7, 13, B) 11, 5, 1, 7, 13, C) 1, 7, 13, 19, D) 6, 1, 4, 9, 13) Harold is going to purchase t-shirts for a school fundraiser, and he is considering two companies. Company A charges $8 per shirt, plus a set-up fee of $100. Company B charges $6 per shirt, plus a set-up fee of $140. At how many shirts would Harold pay the same price for either company? More problems continued on next page

9 14) A landscaping company placed two orders with a nursery. The first order was for 13 bushes and 4 trees, and totaled $487. The second order was for 6 bushes and 2 trees, and totaled $232. The bills do not list the per-item price. Which of the following systems of equations represents this situation, with x representing the number of bushes purchased, and y representing the number of tree purchased? 13xx + 4yy = 487 A) 6xx + 2yy = xx + 4yy = 487 C) xx + yy = xx + 4yy = 232 B) 6xx + 2yy = 487 xx + yy = 487 D) 6xx + 2yy = ) Solve: 3xx 2(xx + 7) = 5xx 14 4xx For #16 18: Water is drained out of a pool, and the graph below shows the depth of the water in the pool at various times x. 16) At one point, leaves clogged up the drain, and no water was being drained out of the pool. At what time did the water first stop draining out of the pool? 17) In order to loosen the leaves clogging up the drain, Extra water was added to the pool. After the leaves were removed from the drain, the water started again draining out of the pool. At what time did the drain start working again? 18) Which of the following statements is true? Choose all that apply. A) The rate of change of the depth of the water was positive for 8 xx 12 minutes. B) The rate of change of the depth of the water was negative for 0 xx 8 minutes. C) The rate of change of the depth of the water was 0 fro 6 xx 8 minutes. D) It took 20 minutes for the water to completely drain out of the pool.

10 Algebra 1 Topic 5 Practice Test Name: Per: For # 1 4, sketch each function, identify the vertex, find the domain and range, and describe the transformation from the parent function. 1) yy = 1 3 xx ) yy = xx 5 3) yy = 2 xx ) yy = 2 xx For #5 6 graph the piecewise function, then write the equation of the absolute value function that is equivalent to the given piecewise function. xx 4, xx < 3 2xx 5, xx < 2 5) ff(xx) = 6) ff(xx) = xx + 2, xx 3 2xx + 3, xx 2 For 7 8, graph. xx 33 iiii xx 11 7) yy = iiii xx > 11 8) f(x) = 11 xx + 11 iiii xx < iiii xx 22

11 9) Which sequence below matches the explicit formula? ff(nn) = 24 5nn A) 24, 19, 14, 9, B) 24, 29, 34, 39, C) 29, 34, 39, 44, D) 19, 14, 9, 4, 10) Provide the property for each step shown in the solution below. Choices: Addition Property of Equality, Subtraction Property of Equality, Multiplication Property of Equality, Division Property of Equality, Distributive Property, Associative Property, Commutative Property Solution Property used 3(4 3xx) = (7 + 5xx) + 2xx Given equation xx = (7 + 5xx) + 2xx xx = 7 + (5xx + 2xx) xx = 7 + 7xx xx = 7 2xx = 19 xx = 19 2 Combine like terms 11) Provide the property for each step shown in the solution below. Solution 5(xx + 3) 2 = 3 5(xx + 3) = Property used Given equation 5(xx + 3) = xx = 1 3 xx = ) The function yy = xx is reflected across the x-axis, vertically compressed by a factor of 1, then translated up 3 4 unit and right 2 units. What is the new equation for the translation? 13) The function yy = xx is reflected across the x-axis, then translated left 3 units and down 4 units. What is the new equation for the translation? 14) Which equation below has a range of yy 2? A) yy = xx 2 B) yy = xx C) yy = xx + 2 D) yy = xx + 2 2

12 15) Which of the following equations best describes the graph shown? A) yy = xx + 3 B) yy = xx 3 C) yy = xx + 3 D) yy = xx 16) What is the range of the absolute value function shown? A) y 1 B) y 1 C) y 0 D) y 0 For # 17 23, solve for xx: 17) 1 4 xx = 2 18) 5 3xx = 18 19) 5xx 1 3 = 4 20) (5xx 2) + 1 = 1 (15xx 9) 21) (2xx 5) = 3xx 5(xx 5) 3 22) Susan is buying black and green olives from the olive bar for her party. She buys 5 lb of olives. Black olives cost $2.00 per pound. Green olives cost $4.00 per pound. She spends $ How many pounds of each type of olive does she buy?

13 For #23 25: Andre drove his car to the store and back. The graph shows the distance he traveled, in miles, as a function of time, in minutes. Fixed the axes labels. 23) At what time did he arrive at the store? 24) How many minutes did he stay at the store? 25) Which of the following statements are true? Choose all that apply. A. Andre was in the store from time t = 5 min to t = 10 min. B. Andre s distance had a negative rate of change for the entire 20 minutes. C. Andre s distance had a positive rate of change for the time t when 0 tt 5 minutes. D. Andre s distance had a rate of change of 0 for the time t when 5 tt 10. Explicit Formula: ff(nn) = ff(1) + (nn 1)dd Recursive Formula: ff(1) =? ; ff(nn) = ff(nn 1) + dd 26) Write a recursive formula for the arithmetic sequence: 1, 5, 9, 13,... A) aa nn = aa nn 1 4; aa 1 = 1 c) aa nn = aa nn 1 + 4; aa 1 = 1 b) aa nn = aa nn 1 + 4; aa 1 = 3 d) aa nn = aa nn 1 4; aa 1 = 3 27) Write a recursive formula for the sequence: Changed to arithmetic sequence: 12, 7, 2, 3, A. ff(1) = 5 and ff(nn) = ff(nn 1) + 12 B. ff(1) = 17 and ff(nn) = ff(nn 1) 5 C. ff(1) = 12 and ff(nn) = ff(nn 1) 5 D. ff(1) = 12 and ff(nn) = ff(nn 1) + 5