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

2. Graphs of Equations

Graphs and Coordinates

College Algebra

2. Graphs of Equations

Graphs and Coordinates

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1:10 minutes

Problem 43

Textbook Question

In Exercises 41–46, use the graph to a. determine the x-intercepts, if any; b. determine the y-intercepts, if any. For each graph, tick marks along the axes represent one unit each.

Verified step by step guidance

Observe the graph and identify the points where the curve crosses the x-axis. These points are the x-intercepts. The x-intercepts occur when the y-value is 0.

From the graph, locate the x-coordinates of the points where the curve intersects the x-axis. These are the x-intercepts.

Next, identify the point where the curve crosses the y-axis. This point is the y-intercept. The y-intercept occurs when the x-value is 0.

From the graph, locate the y-coordinate of the point where the curve intersects the y-axis. This is the y-intercept.

Summarize the x-intercepts and y-intercept based on the observations from the graph.

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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. At these points, the value of y is zero. To find the x-intercepts, one can set the function equal to zero and solve for x. In graphical terms, these are the horizontal intersections of the curve with the x-axis.

Y-Intercepts

Y-intercepts are the points where a graph crosses the y-axis, occurring when the value of x is zero. To determine the y-intercept, substitute x = 0 into the function and solve for y. Graphically, these points represent the vertical intersections of the curve with the y-axis.

Graph Interpretation

Graph interpretation involves analyzing the visual representation of a function to extract meaningful information, such as intercepts, trends, and behavior at extremes. Understanding how to read a graph, including the significance of axes and tick marks, is crucial for accurately identifying intercepts and other features of the function.