Extra Practice

  2. If k(x) = 5x + 2, then what is the value of k(4) − k(1) ?

    1. 15
    2. 17
    3. 19
    4. 21
  3. The function P of X equals absolute value of X, graphed on a coordinate plane. The graph is a V shape that opens upward and has its vertex at the origin. To the left of the vertical axis, the graph passes through the points negative one comma one, negative two comma two, negative three comma three, and so on. To the right of the vertical axis, the graph passes through the points one comma one, two comma two, three comma three, and so on.

  4. The figure shows the function p(x) = | x |. Which statement about the function is not true?

    1. p(0) = 0
    2. p(− 4) = 4
    3. p(4) = − 4
    4. The domain of p(x) is all real numbers.
  5. A graph made up of five line segments that meet at their endpoints. Distance from home, in miles, is plotted along the vertical axis from zero to 8 in increments of one. Time, in minutes, is plotted along the horizontal axis from zero to 60 in increments of 10. The line segments are as follows: the first line segment begins at zero comma zero and increases to the point 15 comma 5. The second line segment is horizontal and extends from 15 comma 5 to 25 comma 5. The third line segment begins at 25 comma 5 and increases to the point 30 comma 7. The fourth line segment is horizontal and extends from 30 comma 7 to 45 comma 7. The final line segment begins at 45 comma 7 and decreases to the point 60 comma zero.

  6. The graph above shows Carmel’s distance from home over a one-hour period, during which time he first went to the library, then went to the grocery store, and then returned home. Which of the following statements could be true?

    1. The grocery store is about 5 miles from Carmel’s house.
    2. Carmel traveled a total of 7 miles from the time he left home until he returned.
    3. The grocery store is 7 miles farther from Carmel’s house than the library is.
    4. Carmel spent 10 minutes at the library and 15 minutes at the grocery store.

  7. If the graph of a function g(x) passes through the point (5, 3), and h(x) is defined as h(x) = −g(x − 2) + 8, through which point does the graph of h(x) pass?

    1. (−3, 11)
    2. (3, 5)
    3. (7, 5)
    4. (7, 11)
  8. x g(x) x h(x)
    −6 −3 0 6
    −3 −2 1 −4
    0 −1 2 2
    3 0 3 0
    6 1 4 −2

  9. Several values for the functions g(x) and h(x) are shown in the tables above. What is the value of g(h(3)) ?

    1. −1
    2.   0
    3.   3
    4.   6

  10. If p is a function defined over the set of all real numbers and p(x + 2) = 3x 2 + 4x + 1, then which of the following defines p(x) ?

    1. p(x) = 3x 2 − 7x + 3
    2. p(x) = 3x 2 − 8x + 5
    3. p(x) = 3x 2 + 16x + 9
    4. p(x) = 3x 2 + 16x + 21

  11. A company uses the function P(x) = 150x − x 2 to determine how much profit the company will make when it sells 150 units of a certain product that sells for x dollars per unit. How much more profit per unit will the company make if it charges $25 for the product than if it charges $20 ?

  12. The customer service department of a wireless cellular provider has found that on Wednesdays, the polynomial function C(t) = −0.0815t 4 + t 3 + 12t approximates the number of calls received by any given time, where t represents the number of hours that have passed since the department opened at 7 AM. Based on this function, how many calls can be expected by 5 PM ?

  13. If g(x) = −2x 2 + 7x − 3, what is the value of g(−2) ?

    1. −25
    2.   −9
    3.   −1
    4.     3

  14. Which of the following does not represent the graph of a function?

  15. A biologist is studying the effect of pollution on the reproduction of a specific plant. She uses the function n(p) to represent these effects, where p is the number of seeds germinated by the test group of the plant over a given period of time. Which of the following lists could represent a portion of the domain for the biologist’s function?

    1. {… −150, −100, −50, 0, 50, 100, 150…}
    2. {−150, −100, −50, 0, 50, 100, 150}
    3. {0, 0.25, 0.5, 0.75, 1, 1.25, 1.5…}
    4. {0, 20, 40, 60, 80…}
  16. An absolute value function, V-shape, graphed on a coordinate plane. The vertex of the V is at negative 3 comma 4 and the V opens downward. The graph crosses the X-axis at negative 7 and at positive 1. The graph crosses the Y-axis at positive 1.

  17. The graph of f (x) is shown above. Which of the following represents the domain and range of the function?

    1. Domain: f(x) ≥ 4; Range: all real numbers
    2. Domain: f(x) ≤ 4; Range: all real numbers
    3. Domain: all real numbers; Range: f(x) ≥ 4
    4. Domain: all real numbers; Range: f(x) ≤ 4

  18. If g(x) = (x − 2)2 − 5, which of the following statements is true?

    1. The function g(x) is increasing over the entire domain.
    2. The function g(x) is decreasing over the entire domain.
    3. The function g(x) is increasing for x < 2 and decreasing for x > 2.
    4. The function g(x) is decreasing for x < 2 and increasing for x > 2.

  19. A function is defined by the equation . For this function, which of the following domain values corresponds to a range value of 14 ?

    1.   − 4
    2.   10
    3.   38
    4. 100

  21. For the piecewise function f (x) defined above, what is the value of f (−3) ?

    1. −3
    2. 7
    3. 10
    4. −3, 7, and 10
  22. Two functions graphed on the same coordinate plane. The graph of F of X consists of part of an upside down parabola and a horizontal line segment. The parabola part of F of X crosses the X-axis at negative 6, has vertex negative two comma 6, and opens downward. It ends at the point two comma negative two, where the horizontal line segment begins and extends to the right. The graph of G of X is a line that increases from left to right and passes through the points negative two comma negative 7, zero comma negative 5, two comma negative 3, and 5 comma zero. The graphs of F and G intersect each other at the point 3 comma negative 2.

  23. Based on the figure above, what is the value of f (−2) + g(2) ?

    1. −3
    2.   0
    3.   3
    4.   6

  24. If f (x) = 3 − x and , which of the following is not in the range of f (g(x)) ?

    1. −3
    2.   0
    3.   2
    4.   4
  25. A piecewise defined function graphed on a coordinate plane. To the left of X equals 4, the function is an upside down V-shape that has vertex zero comma one, and passes through the points negative 1 comma zero and 1 comma zero. This part of the graph ends at an open dot at 4 comma negative 3. To the right of X equals 4, the graph is a horizontal line beginning at the open dot, 4 comma negative 3, and extending to the right.

  26. Which of the following piecewise functions could have been used to generate the graph above?