4.10.1 Analyzing Graphs and Statements in Function Notation

Algebra 14.10.1 Analyzing Graphs and Statements in Function Notation

Search for key terms or text.

Warm Up

This graph shows the populations of Baltimore and Cleveland in the 20th century. $B (t)$ is the population of Baltimore in year t. $C (t)$ is the population of Cleveland in year $t$ .

Line graph showing population trends from 1900 to 2010 for Baltimore (solid blue line) and Cleveland (dashed red line). Both cities peak in mid-1900s, then decline, with Baltimore maintaining a higher population throughout.

Estimate $B (1930)$ and explain what it means in this situation.

Compare your answer:

$B (1930)$ is about 800,000. It’s the population of Baltimore in 1930.

Which statement is true: $B (2000) \geq C (2000)$ or $B (2000) \leq C (2000)$ ?

Answer: $B (2000) \geq C (2000)$

Explain the reasoning for your response to question 2.

Compare your answer:

Your answer may vary, but here is a sample. On the graph, the point that represents $B (2000)$ is located at a higher location than the point that represents $C (2000)$ for each function.

Which statement is true: $B (1900) = C (1900)$ or $B (1900) > C (1900)$ ?

Answer: $B (1900) > C (1900)$

Explain the reasoning for your response to question 4.

Compare your answer:

Your answer may vary, but here is a sample. The blue function representing Baltimore has a higher yue in 1900 than the red-dashed function representing Cleveland does.

Were the two cities’ populations ever the same? If so, when?

Compare your answer:

Yes. The populations were the same in roughly 1910 and 1943.

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/4-10-1-analyzing-graphs-and-statements-in-function-notation

© 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.