Table of contents

0. Review of Algebra4h 16m
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 19m
10. Combinatorics & Probability1h 45m

2. Graphs of Equations

Graphs and Coordinates

College Algebra

2. Graphs of Equations

Graphs and Coordinates

1:17 minutes

Problem 88

Textbook Question

In Exercises 85–90, find the x-intercepts of the graph of each equation. Then use the x-intercepts to match the equation with its graph. [The graphs are labeled (a) through (f).] y = x^(-2) - x^(-1) - 6

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Key Concepts

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

X-Intercepts

X-intercepts are the points where a graph crosses the x-axis, which occur when the value of y is zero. To find the x-intercepts of an equation, you set the equation equal to zero and solve for x. In this case, you would solve the equation y = x^(-2) - x^(-1) - 6 by finding the values of x that satisfy this condition.

Rational Functions

The given equation involves rational functions, which are expressions formed by the ratio of two polynomials. In this case, x^(-2) and x^(-1) can be rewritten as 1/x^2 and 1/x, respectively. Understanding the behavior of rational functions, including their asymptotes and intercepts, is crucial for analyzing their graphs and determining their x-intercepts.

Graph Matching

Matching an equation to its graph involves understanding the characteristics of the graph, such as its shape, intercepts, and asymptotic behavior. After finding the x-intercepts, you can compare these points with the graphs labeled (a) through (f) to identify which graph corresponds to the given equation. This process requires visual interpretation and knowledge of how different equations manifest graphically.