Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

3. Functions

Intro to Functions & Their Graphs

College Algebra

3. Functions

Intro to Functions & Their Graphs

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0:53 minutes

Problem 44

Textbook Question

Graph each equation. ƒ(x) = 3

Verified step by step guidance

Step 1: Understand the equation. The equation ƒ(x) = 3 is a constant function. This means that for any value of x, the value of ƒ(x) will always be 3.

Step 2: Identify the type of graph. Since ƒ(x) = 3 is a constant function, its graph will be a horizontal line.

Step 3: Plot the graph. To plot the graph, you can start by drawing a horizontal line at y = 3 on the coordinate plane. This line represents all the points where the y-coordinate is 3, regardless of the x-coordinate.

Step 4: Label the graph. It's important to label your graph with the equation ƒ(x) = 3, so that anyone looking at it will know what it represents.

Step 5: Review the graph. Make sure your graph is a horizontal line at y = 3, and that it's labeled correctly. This graph represents all the solutions to the equation ƒ(x) = 3.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Constant Functions

A constant function is a type of function where the output value remains the same regardless of the input value. In the case of ƒ(x) = 3, the function outputs the value 3 for every x in its domain. This results in a horizontal line on the graph, indicating that no matter what x-value is chosen, the y-value will always be 3.

Graphing Functions

Graphing functions involves plotting points on a coordinate plane to visually represent the relationship between the input (x) and output (y) values. For the function ƒ(x) = 3, you would plot points such as (0, 3), (1, 3), and (-1, 3), all of which lie on the same horizontal line. Understanding how to graph functions is essential for visualizing their behavior.

Coordinate Plane

The coordinate plane is a two-dimensional surface defined by a horizontal axis (x-axis) and a vertical axis (y-axis). Each point on the plane is represented by an ordered pair (x, y). In graphing the function ƒ(x) = 3, recognizing how to locate points on the coordinate plane is crucial, as it allows for the accurate representation of the function's output across different input values.

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