5.12.4 Possible Equation for a Function on a Graph

Algebra 15.12.4 Possible Equation for a Function on a Graph

Search for key terms or text.

Cool Down

Examine the three graphs representing three exponential functions: $f$ , $g$ , and $h$ .

Line graph showing three upward-curving lines labeled a (blue), b (green), and c (orange) on axes labeled x (horizontal) and y (vertical), with values increasing rapidly as x increases. h and g intersect on the y-axis and f is below both of them with a wider curve. h is a steeper curve than g. The lines are h, g, and then f across the graph.

The functions $f$ and $h$ are defined as:

$f (x) = 10 \cdot 2^{x}$
$h (x) = 20 \cdot 4^{x}$

Which of the following could define function $g$ ? Be prepared to show your reasoning.

Multiple Choice:

$g (x) = 20 \cdot (1.5)^{x}$

$g (x) = 20 \cdot (2.5)^{x}$

$g (x) = 10 \cdot (3.5)^{x}$

$g (x) = 20 \cdot (4.5)^{x}$

$g (x) = 20 \cdot (2.5)^{x}$ .

Explain your reasoning.

Compare your answer:

The graph of $g$ has the same $y$ -intercept as the graph of $h$ , which is 20. It grows more quickly than $f$ but more slowly than $h$ , so the growth factor must be greater than 2 but less than 4.

Previous Next

Citation/Attribution

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 permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution-NonCommercial-ShareAlike License and you must attribute OpenStax.

Attribution information

If you are redistributing all or part of this book in a 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 digital format, then you must 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

Use the information below to generate a citation. We recommend using a citation tool such as this one.
- Authors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis, Jay Abramson, Sharon North, Amy Baldwin, Alyssa Howell
- Publisher/website: OpenStax
- Book title: Algebra 1
- Publication date: Jun 4, 2025
- Location: Houston, Texas
- Book URL: https://openstax.org/books/algebra-1/pages/about-this-course
- Section URL: https://openstax.org/books/algebra-1/pages/5-12-4-possible-equation-for-a-function-on-a-graph

© May 21, 2025 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 are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.