Questions: Determine whether the graph is that of a function by using the vertical-line test. In either case, use the graph to find the following. (a) The domain and range (b) The intercepts, if any (c) Any symmetry with respect to the x-axis, y-axis, or the origin Is the graph that of a function? A. No, the graph is not a function because a vertical line x=2 intersects the graph at two points. B. No, the graph is not a function because a vertical line x=2 intersects the graph at only one point. C. Yes, the graph is a function because every vertical line intersects the graph in at most one point. D. Yes, the graph is a function because every vertical line intersects the graph in more than one point. (a) The domain is (Type your answer in interval notation.)

Determine whether the graph is that of a function by using the vertical-line test. In either case, use the graph to find the following. (a) The domain and range (b) The intercepts, if any (c) Any symmetry with respect to the x-axis, y-axis, or the origin Is the graph that of a function? A. No, the graph is not a function because a vertical line x=2 intersects the graph at two points. B. No, the graph is not a function because a vertical line x=2 intersects the graph at only one point. C. Yes, the graph is a function because every vertical line intersects the graph in at most one point. D. Yes, the graph is a function because every vertical line intersects the graph in more than one point. (a) The domain is (Type your answer in interval notation.)
Transcript text: Determine whether the graph is that of a function by using the vertical-line test. In either case, use the graph to find the following. (a) The domain and range (b) The intercepts, if any (c) Any symmetry with respect to the $x$-axis, $y$-axis, or the origin Is the graph that of a function? A. No, the graph is not a function because a vertical line $x=2$ intersects the graph at two points. B. No, the graph is not a function because a vertical line $x=2$ intersects the graph at only one point. C. Yes, the graph is a function because every vertical line intersects the graph in at most one point. D. Yes, the graph is a function because every vertical line intersects the graph in more than one point. (a) The domain is $\square$ (Type your answer in interval notation.)
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Solution

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Solution Steps

Step 1: Determine if the graph represents a function

The vertical line test helps determine if a graph is a function. If any vertical line intersects the graph more than once, the graph is not a function. In this case, the vertical line x=2 intersects the graph at two points, (2,4) and (2,-4).

Step 2: Select the correct multiple-choice answer

Since the vertical line x=2 intersects the graph at two points, the graph does not represent a function. The correct answer is A.

Step 3: Find the domain

The domain of a graph is all possible x-values. This graph has arrows pointing downwards at both ends, meaning that x extends infinitely in both directions.

Final Answer:

The graph is not a function. The correct multiple choice answer is A. The domain is (-∞,∞).

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