Skip to ContentGo to accessibility page
OpenStax Logo
Algebra 1

5.15.5 Practice

Algebra 15.15.5 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 .

  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?


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 ) ?


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.
PreviousNext
Order a print copy
Citation/Attribution
Reuse and redistribution of this content in digital or print format:
  • This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's prior written permission.
  • This book uses the Creative Commons Attribution-NonCommercial-ShareAlike License, which means that you can reuse and modify the material only for noncommercial purposes, must attribute OpenStax, and must distribute any derivative works under the same license.
  • Any commercial printing of this textbook, including using a local or custom printer, must be approved by OpenStax, and proper citation provided.
  • OpenStax-copyrighted images, activities, assessments, and similar components of this book are subject to the same licensing – CC-BY-NC-SA. They can be used for noncommercial purposes with attribution. Commercial use requires permission.
  • Permission requests: Anyone who intends to incorporate this content (including text, images, and other components) into large language models, use it in AI offerings, use it commercially (including in print), and/or has questions about another use case is welcome to complete our reuse request form.
Attribution information
  • If you are redistributing all or part of this book in a noncommercial print format, then you must include on every physical page the following attribution:

    Access for free at https://openstax.org/books/algebra-1/pages/about-this-course

  • If you are redistributing all or part of this book in a noncommercial digital format, then for every page that includes OpenStax content, you must license the derivative work under the same CC-BY-NC-SA license as the original, and include on every digital page view the following attribution:

    Access for free at https://openstax.org/books/algebra-1/pages/about-this-course

Citation information

The information below includes the information needed to generate citations in most major styles (APA, MLA, etc.); you must reformat and organize the information as needed to fit the requirements of the style. Use the information below to generate a citation. We recommend using a citation tool such as this one.

© Apr 23, 2026 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License. The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo, and Rice University name, and Rice University logo trademarks, or wordmarks are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.