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Ch. 2 - Graphs and Functions
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 2 - Graphs and FunctionsProblem 21
Chapter 3, Problem 21

For each graph, determine whether y is a function of x. Give the domain and range of each relation.
Graph showing two parabolas, one opening upward above y=0 and one opening downward below y=0, on an xy-plane.

Verified step by step guidance
1
Step 1: Identify if y is a function of x by using the vertical line test. A relation is a function if and only if no vertical line intersects the graph at more than one point.
Step 2: Observe the graph. Notice that for some values of x, there are two corresponding y-values (for example, at x = 0, y = 11 and y = -11). This means the vertical line at x = 0 intersects the graph at two points.
Step 3: Since the vertical line at x = 0 intersects the graph at two points, y is not a function of x for this relation.
Step 4: Determine the domain by looking at the x-values covered by the graph. The graph extends horizontally from about -20 to 20, so the domain is approximately \([-20, 20]\).
Step 5: Determine the range by looking at the y-values covered by the graph. The graph extends vertically from about -20 to 20, so the range is approximately \([-20, 20]\).

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Key Concepts

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

Definition of a Function

A function is a relation where each input (x-value) corresponds to exactly one output (y-value). This means no vertical line intersects the graph at more than one point. Understanding this helps determine if y is a function of x by checking if any x-value maps to multiple y-values.
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Domain and Range

The domain of a relation is the set of all possible x-values, while the range is the set of all possible y-values. Identifying these sets from a graph involves looking at the horizontal spread for the domain and the vertical spread for the range.
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Vertical Line Test

The vertical line test is a visual method to determine if a graph represents a function. If any vertical line drawn through the graph intersects it more than once, the graph does not represent a function. This test is essential for analyzing the given parabolic curves.
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Related Practice
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Textbook Question

For each graph, determine whether y is a function of x. Give the domain and range of each relation.

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Textbook Question

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