Functions & Graphing

In Functions & Graphing topic, 9th Grade students will learn how to describe relationships where one input produces one output and how to represent that relationship using tables, equations, and graphs. Students interpret slope as a rate of change and intercepts as starting values. They learn to read graphs carefully and connect graph shapes to situations. Students also practice writing function rules and evaluating them for specific inputs.

What Children Learn

Students learn function vocabulary such as input, output, domain, and range. They practice evaluating functions and creating tables from a rule. Students learn graph features like intercepts, slope, and intervals where the graph increases or decreases. They connect real context to graphs, such as cost over time or distance over time. Students learn to decide whether a relation is a function using the one input to one output idea. Students also practice comparing two functions by comparing their rates of change and starting points.

Sample Questions Children Practice

1. If f(x) = 3x - 2, what is f(5)?

A. 11

B. 13

C. 15

D. 17

2. Fill in the blank: The slope of a line is the ____ of change in y divided by the change in x.

3. A line passes through (0, 4) and (2, 10). What is its slope?

A. 2

B. 3

C. 4

D. 6

4. Thinking question: Two functions start at the same y intercept. One has slope 2 and one has slope 5. What will happen to their y values as x increases?

Why This Topic Matters

Functions help students describe how things change. Graphing builds visual understanding and supports prediction. These skills are used in science, economics, and technology whenever relationships need to be modeled and compared.