Big Ideas Math 2015 HS Algebra 1: Common Core Edition Chapter 10 Test

Transcription

1 Big Ideas Math 2015 HS Algebra 1: Common Core Edition Chapter 10 Test Exercise 1 Plot the points on the graph of x f (x)????? f (x) = x + 5 that correspond to the x-values shown in the table. Point Move Undo Redo Reset Exercise 2 1 of 8 5/18/17, 7:36 AM

2 Compare the graph of g (x) = x 6 to the graph of f (x) = x. The graph of g is a and a of the graph of f. reflection in the x-axis reflection in the y-axis horizontal stretch by a factor of 6 horizontal shrink by a factor of 1 6 vertical stretch by a factor of 6 vertical shrink by a factor of 1 6 translation 6 units right translation 6 units left translation 6 units up translation 6 units down Exercise 3 Identify the graph of g (x) = 3 x Exercise 4 Compare the graph of g (x) = 3 x 4 to the graph of f (x) = x. 3 The graph of g is a translation unit(s) of the graph of f. Exercise 5 2 of 8 5/18/17, 7:36 AM

3 Which of the following describes the transformation from the graph of f (x) = g (x) = 3 2x + 4? 3 x to the graph of The graph of g is a reflection in the y-axis followed by a horizontal stretch by a factor of 2 and a translation 4 units up of the graph of f. 1 The graph of g is a reflection in the y-axis followed by a horizontal shrink by a factor of and a 2 translation 4 units up of the graph of f. The graph of g is a reflection in the y-axis and a vertical stretch by a factor of 2, followed by a translation 4 units up of the graph of f. 1 The graph of g is a reflection in the x-axis followed by a horizontal shrink by a factor of and a 2 translation 4 units up of the graph of f. Exercise 6 The graph of cube root function m is shown. Compare the average rate of change of m to the average rate of change of h (x) = 2 3 x over the interval x = 0 to x = 8. The average rate of change of m is times the average rate of change of h over the interval x = 0 to x = 8. Exercise 7 3 of 8 5/18/17, 7:36 AM

4 Solve 3 x = 4. The solution is x =. Exercise 8 Solve 4x 3 = 3x The solution is x =. Exercise 9 Solve 9x + 35 = 5. 3 The solution is x =. Exercise 10 Identify the solution(s) of 2x = 4x + 8. x = 5 x = 4 x = 3 x = 2 x = 1 x = 0 x = 1 x = 2 x = 3 x = 4 x = 5 Exercise 11 4 of 8 5/18/17, 7:36 AM

5 Match each relation with its inverse. (4, 3), (3, 4) (3, 4), (4, 3) (3, 4), (4, 3) (4, 3), (3, 4) (3, 4), (4, 3) (3, 4), (4, 3) (4, 3), (3, 4) (4, 3), (3, 4) Exercise 12 Let f (x) = 5x + 1. Solve y = f (x) for x. x = Exercise 13 Find the inverse of f (x) = 7x The inverse of f is g(x) =. Exercise 14 Find the inverse of f (x) = 16x 2 3, x 0. The inverse of f is g(x) =. Exercise 15 5 of 8 5/18/17, 7:36 AM

6 Identify the inverse of each function. Then indicate whether the inverse is a function. The inverse of f (x) = (x + 5) 2 is g (x) =. The inverse is. The inverse of f (x) = x + 5 is g (x) =. The inverse is. The inverse of f (x) = x is g (x) =. The inverse is. The inverse of f (x) = x + 5 is g (x) =. The inverse is. (x 5) 2, x 5 x 2 5, x 0 ± x 5 ± x 5 a function not a function Exercise 16 Let g be the inverse of f (x) = x 2. Use the graph of f to determine whether each statement is true or false. The inverse of f is a function. True False The equation f (x) = g (x) has exactly one real solution. True False The domain of g is x 0. True False The range of g is all real numbers. True False Exercise 17 6 of 8 5/18/17, 7:36 AM

7 The model v (d) = 2gd represents the velocity v (in meters per second) of a free-falling object on Jupiter, where g is the constant 23.1 meters per second squared and d is the distance (in meters) the object has fallen. The velocity of a free-falling object on Earth is shown in the graph. Compare the velocities by finding and interpreting their average rates of change over the interval d = 0 to d = 30. From 0 to 30 meters, the velocity of a free-falling object increases at an average rate of about meter(s) per second per meter on Earth and about meter(s) per second per meter on Jupiter. Exercise 18 The velocity v (in meters per second) of a tsunami can be modeled by the function v (x) = 9.8x, where x is the water depth (in meters). At what depth does the velocity of the tsunami exceed 125 meters per second? Round your answer to the nearest meter. The velocity exceeds 125 meters per second at a depth of about meters. Exercise 19 The shoulder height h (in centimeters) of a male Asian elephant can be modeled by the function h = t , where t is the age (in years) of the elephant. Estimate the age of an elephant whose shoulder height is 185 centimeters. The elephant is about years old. Exercise 20 7 of 8 5/18/17, 7:36 AM

8 L The period P (in seconds) of a pendulum is given by the function P = 2π, where L is the pendulum length (in feet). What is the length of a pendulum with a period of 0.75 second? Round your answer to the nearest hundredth of a foot. 32 The pendulum has a length of about feet. 8 of 8 5/18/17, 7:36 AM