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Practice

5.15.5 Practice

5.15.5 • Practice

Complete the following questions to practice the skills you have learned in this lesson.

  1. Whenever the input of a function f increases by 1, the output increases by 5. Which of these equations could define f ?
  1. f ( x ) = x 5
  2. f ( x ) = 5 x
  3. f ( x ) = 5 x + 3
  4. f ( x ) = 3 x + 5
  1. The function f is defined by f ( x ) = 2 x . Which of the following statements is true about the values of f ? Select the two statements that apply.
  1. When the input x increases by 1, the value of f increases by 2.
  2. When the input x increases by 1, the value of f increases by a factor of 2.
  3. When the input x increases by 3, the value of f increases by 8.
  4. When the input x increases by 3, the value of f increases by a factor of 8.
  5. When the input x increases by 4, the value of f increases by a factor of 4.
Use the graph below for questions 3 and 4.

The two lines on the coordinate plane are graphs of functions f and g .

Graph of 2 lines.

  1. Use the graph to explain why the value of f increases by 2 each time the input x increases by 1.
  1. The y -axis counts by 2’s so f must increase 2 each time the input increases 1.
  2. There are two graphs so f increases by 2 each time the input x increases by 1.
  3. ( 0 , 0 ) and ( 1 , 2 ) are two points on the graph of f . Between the two points, y increases by 2 and x increases by 1.
  4. f does not increase by 2 each time x increases by 1.
  1. Use the graph to explain why the value of g increases by 2 each time the input x increases by 1. Select two that apply.
  1. f and g never intersect and stay an equal distance apart. f increases by 2 every time x increases by 1, so g must do so as well.
  2. You can’t use the graph because the points are not labeled.
  3. There are two graphs so g increases by 2 each time the input x increases by 1.
  4. ( 0 , 5 ) and ( 1 , 7 ) are points on the graph of g . Between the two points, y increases by 2 and x increases by 1.
  5. ( 0 , 0 ) and ( 1 , 2 ) are two points on the graph of g . Between the two points, y increases by 2 and x increases by 1.
  1. The function h is given by h ( x ) = 5 x . Find the quotient h ( x + 2 ) h ( x ) . 
  1. The function h is given by h ( x ) = 5 x . Find the quotient h ( x + 3 ) h ( x ) .
  1. 125
  2. 25
  3. 15
  4. 5
  1. For each of the functions f , g , h , p , and q , the domain is 0 ≤ x ≤ 100 . For which functions is the average rate of change a good measure of how the function changes for this domain? Select three that apply. 
  1. f ( x ) = x + 2
  2. g ( x ) = 2 x
  3. h ( x ) = 111 x − 23
  4. p ( x ) = 50 , 000 ⋅ 3 x
  5. q ( x ) = 87.5
  1. What would be the rate of change of the following table?


    2. x f ( x )
    1 -4
    2 -2
    3 0
    4 2
    5 4

  1. Given the following table, what would be f ( x + 2 ) f ( x + 1 ) ?


    2. x f ( x )
    1 2
    2 4
    3 8
    4 16
    5 32
  1. Which of the following statements compare rates of f ( x ) = 3 x + 2 and g ( x ) = 3 x ?
  1. In g you add 3 to get to the next term; in f you multiply by 3 to get to the next term.
  2. In f you add 3 to get to the next term; in g you multiply by 3 to get to the next term.
  3. In f and g you add 3 to get to the next term.
  4. In f and g you multiply by 3 to get to the next term.