Ch. 2 - Functions and Graphs

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

Blitzer 8th Edition

Ch. 2 - Functions and Graphs

Problem 78

Chapter 3, Problem 78

Use the graph to determine a.the x-intercepts, if any; b. the y-intercept, if any; and e. the missing function values, indicated by question marks, below each graph.

Verified step by step guidance

Identify the x-intercepts by finding the points where the graph crosses the x-axis. These are points where the y-value is zero. From the graph, note the x-values at these points.

Identify the y-intercept by finding the point where the graph crosses the y-axis. This is the point where the x-value is zero. From the graph, note the y-value at this point.

To find the missing function values indicated by question marks, locate the corresponding x-values on the graph and determine the y-values by reading the height of the graph at those points.

Write down the coordinates of the x-intercepts and y-intercept clearly in the form \((x, 0)\) for x-intercepts and \((0, y)\) for the y-intercept.

Use the identified points to understand the behavior of the function and verify the missing values by checking if they align with the shape and trend of 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 points where the graph crosses the x-axis, meaning the y-value is zero at these points. Identifying x-intercepts involves finding the values of x for which the function equals zero. In the graph, these are marked as (0,0) and (5,0).

Y-Intercept

The y-intercept is the point where the graph crosses the y-axis, which occurs when x equals zero. This point shows the initial value of the function. In the graph, the y-intercept is at (0,7), indicating the function's value when x is zero.

Reading Function Values from a Graph

To determine missing function values, analyze the graph's points and their coordinates. Each point on the curve corresponds to an (x, y) pair, where y is the function value at x. Using the graph, you can estimate or identify exact values to fill in missing data.

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