Questions: Question 6 of 6 This quiz 6 point(s) possible This question: 1 point(s) p 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 C. Yes, the graph is a function because every vertical line intersects the graph in more than one point. D. No, the graph is not a function because a vertical line x=pi/2 intersects the graph at two points. (a) The domain is . (Type your answer in interval notation.) The range is . (Type your answer in interval notation.) (b) Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. The intercepts are (-pi, 0),(0,0),(pi, 0). (Type an ordered pair. Type an exact answer, using pi as needed. Use a comma to separate answers as needed.) B. There are no intercepts. (c) Select all that apply. A. It is symmetrical with respect to the x-axis. B. It is symmetrical with respect to the y-axis. C. It is symmetrical with respect to the origin. D. The graph is not symmetrical.

Question 6 of 6 This quiz 6 point(s) possible This question: 1 point(s) p 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 C. Yes, the graph is a function because every vertical line intersects the graph in more than one point. D. No, the graph is not a function because a vertical line x=pi/2 intersects the graph at two points. (a) The domain is . (Type your answer in interval notation.) The range is . (Type your answer in interval notation.) (b) Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. The intercepts are (-pi, 0),(0,0),(pi, 0). (Type an ordered pair. Type an exact answer, using pi as needed. Use a comma to separate answers as needed.) B. There are no intercepts. (c) Select all that apply. A. It is symmetrical with respect to the x-axis. B. It is symmetrical with respect to the y-axis. C. It is symmetrical with respect to the origin. D. The graph is not symmetrical.
Transcript text: Question 6 of 6 This quizz 6 point(s) possit This question: 1 point(s) $p$ 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 C. Yes, the graph is a function because every vertical line intersects the graph in more than one point. D. No, the graph is not a function because a vertical line $x=\frac{\pi}{2}$ intersects the graph at two points. (a) The domain is ]. $\square$ (Type your answer in interval notation.) The range is $\square$ . (Type your answer in interval notation.) (b) Select the correct choice and, if necessary, fill in the answer box to complete your choice. $\qquad$ A. The intercepts are $(-\pi, 0),(0,0),(\pi, 0)$. (Type an ordered pair. Type an exact answer, using $\pi$ as needed. Use a comma to separate answers as needed.) B. There are no intercepts. (c) Select all that apply. A. It is symmetrical with respect to the $x$-axis. B. It is symmetrical with respect to the $y$-axis. C. It is symmetrical with respect to the origin. D. The graph is not symmetrical.
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Solution

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Solution Steps

Step 1: Determine if the graph is a function using the vertical-line test
  • The vertical-line test states that if any vertical line intersects the graph at more than one point, the graph is not a function.
  • Observing the graph, a vertical line at \( x = -\frac{\pi}{2} \) intersects the graph at two points.
  • Therefore, the graph is not a function.
Step 2: Identify the domain and range
  • The domain of the graph is the set of all possible \( x \)-values. From the graph, the \( x \)-values range from \(-\pi\) to \(\pi\).
  • The range of the graph is the set of all possible \( y \)-values. From the graph, the \( y \)-values range from \(-1\) to \(1\).
Step 3: Identify the intercepts
  • The intercepts are the points where the graph intersects the axes.
  • From the graph, the intercepts are at \( (-\pi, 0) \), \( (0, 0) \), and \( (\pi, 0) \).

Final Answer

  • The graph is not a function because a vertical line \( x = -\frac{\pi}{2} \) intersects the graph at two points.
  • The domain is \([- \pi, \pi]\).
  • The range is \([-1, 1]\).
  • The intercepts are \((- \pi, 0)\), \((0, 0)\), and \((\pi, 0)\).
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