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Algebra 1

5.15.5 Practice

Algebra 15.15.5 Practice

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

Double click on mathematical expressions/equations to enlarge. If needed, use the “^” symbol to enter an exponent.
  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 all 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.

The two lines on the coordinate plane are graphs of functions f and g . Use for the graph below for questions 3 and 4.

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. 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.
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