Questions: Chapter 4 Homework Question 13, 4.1.35 HW Score: 28%, 42 of 150 points Part 1 of 2 Points: 0 of 2 Determine visually whether the graph is symmetric about the x-axis, the y-axis, or neither. If the graph represents a function, determine whether the function is even, odd, or neither. Is the graph symmetric about the x-axis, the y-axis, or neither? Select all that apply. A. The graph is symmetric about the y-axis. B. The graph is symmetric about the x-axis. C. The graph is symmetric about neither the x-axis nor the y-axis.

Chapter 4 Homework
Question 13, 4.1.35
HW Score: 28%, 42 of 150 points
Part 1 of 2
Points: 0 of 2

Determine visually whether the graph is symmetric about the x-axis, the y-axis, or neither. If the graph represents a function, determine whether the function is even, odd, or neither.

Is the graph symmetric about the x-axis, the y-axis, or neither? Select all that apply.
A. The graph is symmetric about the y-axis.
B. The graph is symmetric about the x-axis.
C. The graph is symmetric about neither the x-axis nor the y-axis.

Transcript text: Chapter 4 Homework Question 13, 4.1.35 HW Score: $28 \%, 42$ of 150 points Part 1 of 2 Points: 0 of 2 Save Determine visually whether the graph is symmetric about the $x$-axis, the $y$-axis, or neither. If the graph represents a function, determine whether the function is even, odd, or neither. Is the graph symmetric about the $x$-axis, the $y$-axis, or neither? Select all that apply. A. The graph is symmetric about the $y$-axis. B. The graph is symmetric about the $x$-axis. C. The graph is symmetric about neither the $x$-axis nor the $y$-axis.

Solution

Solution Steps

Step 1: Determine Symmetry about the x-axis

To check if the graph is symmetric about the x-axis, we reflect the graph over the x-axis. If the graph remains unchanged, it is symmetric about the x-axis. In this case, reflecting the graph over the x-axis does not result in the same graph.

Step 2: Determine Symmetry about the y-axis

To check if the graph is symmetric about the y-axis, we reflect the graph over the y-axis. If the graph remains unchanged, it is symmetric about the y-axis. In this case, reflecting the graph over the y-axis does not result in the same graph.

Step 3: Determine if the Graph is Symmetric about Neither Axis

Since the graph is not symmetric about either the x-axis or the y-axis, we conclude that the graph is symmetric about neither axis.