Ch. 2 - Functions and Graphs

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

Blitzer 8th Edition

Ch. 2 - Functions and Graphs

Problem 77

Chapter 3, Problem 77

In Exercises 77–92, 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

Step 1: Identify the x-intercepts of the graph. The x-intercepts are the points where the graph crosses the x-axis. From the graph, these points are (-8, 0) and (10, 0).

Step 2: Identify the y-intercept of the graph. The y-intercept is the point where the graph crosses the y-axis. From the graph, this point is (0, 8).

Step 3: Analyze the missing function values indicated by question marks. For each missing value, locate the corresponding x-coordinate on the graph and determine the y-coordinate by observing the graph's behavior at that point.

Step 4: For example, if a missing value corresponds to x = 0, the y-coordinate is 8, as determined from the graph. Similarly, if a missing value corresponds to x = -8 or x = 10, the y-coordinate is 0.

Step 5: Summarize the findings: The x-intercepts are (-8, 0) and (10, 0), the y-intercept is (0, 8), and the missing function values can be determined by observing the graph at the specified x-coordinates.

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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, indicating where the function's output (y-value) is zero. To find x-intercepts, set the function equal to zero and solve for x. In the provided graph, the x-intercepts are located at the points (-8, 0) and (10, 0).

Y-Intercept

The y-intercept is the point where a graph intersects the y-axis, representing the value of the function when x is zero. To determine the y-intercept, evaluate the function at x = 0. In the graph, the y-intercept is at the point (0, 8), indicating that the function's value is 8 when x is zero.

Function Values

Function values refer to the outputs of a function for specific inputs. In the context of the graph, missing function values can be identified by observing the graph at given x-values. For instance, the graph shows a missing value at (0, -10), which indicates that the function's output is -10 when x is 0, highlighting the importance of analyzing the graph's behavior.

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