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

Previous problemNext problem

1:17 minutes

Problem 41

Textbook Question

Graph each equation. ƒ(x) = x

Verified step by step guidance

Step 1: Understand the equation. The equation given is ƒ(x) = x. This is a linear equation, which means it will graph as a straight line. The slope of the line is 1 and the y-intercept is 0.

Step 2: Draw a set of axes. Label the x-axis and the y-axis. The x-axis represents the input values (x) and the y-axis represents the output values (ƒ(x)).

Step 3: Plot the y-intercept. The y-intercept is the point where the line crosses the y-axis. Since the y-intercept is 0, plot a point at (0,0).

Step 4: Use the slope to find another point. The slope is the ratio of the change in y to the change in x. Since the slope is 1, this means that for every 1 unit increase in x, y also increases by 1 unit. So, from the y-intercept (0,0), move 1 unit to the right and 1 unit up to plot the point (1,1).

Step 5: Draw the line. Once you have at least two points, you can draw a straight line through them. This line represents the graph of the equation ƒ(x) = x.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Play a video:

Was this helpful?

Key Concepts

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

Function Definition

A function is a relation that assigns exactly one output for each input from its domain. In the case of ƒ(x) = x, the function maps every real number to itself, illustrating a direct linear relationship. Understanding this concept is crucial for interpreting how inputs and outputs relate in a graph.

Graphing Linear Functions

Graphing linear functions involves plotting points that satisfy the equation on a coordinate plane. For ƒ(x) = x, the graph is a straight line that passes through the origin (0,0) with a slope of 1. This means for every unit increase in x, y also increases by one unit, creating a 45-degree angle with the axes.

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). Understanding how to navigate this plane is essential for accurately graphing functions and interpreting their behavior visually.

Watch next

Master Relations and Functions with a bite sized video explanation from Patrick

Start learning