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Question

Which graph shows line symmetry about the y-axis? On a coordinate plane, a curve is asymptotic to the x-axis and y-axis in quadrant 4. On a coordinate plane, a curve goes through one and one-half cycles. For the first curve, the maximum is at (negative 3, 1) and the minimum is (0, negative 1). For the half curve, the maximum is at (3, 1). On a coordinate plane, two straight lines connect at (0, 0). The first line has a negative slope and goes through (negative 1, 3). The second line has a negative slope and goes through (3, negative 1). On a coordinate plane, a curve has a minimum point at (negative 2.5, negative 5) and a maximum point at (2.5, 5).

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Stanley

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Solution By Steps

Step 1: Define Line Symmetry About the Y-axis

Line symmetry about the y-axis means that for every point (x, y) on the graph, there is a corresponding point (-x, y) also on the graph.

Step 2: Analyze Graph 1

A curve asymptotic to the x-axis and y-axis in quadrant 4 does not imply symmetry about the y-axis.

Step 3: Analyze Graph 2

A curve going through one and one-half cycles with specified maxima and minima does not guarantee symmetry about the y-axis.

Step 4: Analyze Graph 3

Two straight lines with negative slopes intersecting at the origin could be symmetric about the y-axis if they are mirror images of each other across the y-axis.

Step 5: Analyze Graph 4

A curve with a minimum at (-2.5, -5) and a maximum at (2.5, 5) suggests symmetry about the y-axis because the x-coordinates are opposites and the y-coordinates are the same.

Final Answer

The graph that shows line symmetry about the y-axis is the one with a curve that has a minimum point at (-2.5, -5) and a maximum point at (2.5, 5).

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