Symmetry — Quiz

Question 4 • Algebra II

Which graph shows line symmetry about the y -axis?

Answer

Image with description On a coordinate plane, the x and y axes range from negative 5 to 5 in increments of 1. The graph has a curve k of x with three x-intercepts at (negative 4 comma 0), (0 comma 0), and (4 comma 0). The curve starts in the second quadrant, goes down to the third quadrant, moves up and goes to the first quadrant, and finally goes to the fourth quadrant.

Image with description On a coordinate plane, the x and y axes range from negative 5 to 5 in increments of 1.The graph has a curve f of x in the fourth quadrant which is asymptotic to the x-axis and y-axis.

Image with description On a coordinate plane, the x and y axes range from negative 5 to 5 in increments of 1. The graph has a v-shaped curve h of x that has a vertex at (0 comma 0). The left side line has a negative slope and goes through (negative 1 comma 3). The right side line has a negative slope and goes through (3 comma negative 1).

Image with description On a coordinate plane, the x and y axes range from negative 5 to 5 in increments of 1. The graph has a curve g of x with crests and troughs. The crests are at (negative 3 comma 1), and (3 comma 1), and trough at (0 comma negative 1). The curve has 4 x-intercepts.

Explanation

A graph has symmetry about the y-axis when the part to the left of the axis is a mirror image of the part to the right. In D, the crests at (−3, 1) and (3, 1) are equally far from the y-axis and have the same height, and the trough is on the y-axis at (0, −1). So the graph showing line symmetry about the y-axis is the one with crests at (−3, 1) and (3, 1).

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