Question

On a coordinate plane, a graph of a polynomial function has two curves and one turning point. The first curve intercepts the x-axis at -1 and the second curve intercepts the x-axis at 1. On a coordinate plane, a sine curve goes through one cycle. What type of symmetry do these functions have?

1) No symmetry
2) Vertical symmetry
3) Horizontal symmetry
4) Both vertical and horizontal symmetry

Answer 1

Both the described polynomial function with two x-intercepts and one turning point and the sine curve have vertical symmetry about their respective central axes.

Step-by-step explanation:

The question you have asked is about determining the type of symmetry present in two different functions represented on a coordinate plane: a polynomial function with two curves and one turning point, and a sine curve that goes through one cycle.

For the polynomial function that intercepts the x-axis at -1 and 1, if we assume that the polynomial is quadratic, it would have vertical symmetry because it would be symmetrical about the line x = 0, which is the vertical line passing through the turning point that lies exactly between the x-intercepts.

The sine curve, being a periodic function with a full cycle present, would also have vertical symmetry about its central axis, which would coincide with a vertical line passing through the peak and trough of one cycle midway at the phase shift.

Based on this information, the answer to the question is option 2) Vertical symmetry.