Ch. 1 - Equations and Inequalities

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

Blitzer 8th Edition

Ch. 1 - Equations and Inequalities

Problem 43a

Chapter 2, Problem 43a

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.

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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.

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