Question

HELP!!!!!!!

The graph of a piecewise function is shown.

The graph shows a piecewise function in 3 pieces. The first piece is curved and increasing from the left through negative 3 comma negative 5 with a closed endpoint at negative 2 comma 0. The second piece is linear with an open endpoint at negative 2 comma 1 and another open endpoint at 2 comma negative 1. The third piece is curved with an endpoint at 2 comma 0, and it goes through the point 3 comma 5 and continues to increase to the right.

What is the asymptote(s) of the function?

y = 0
x = −2, x = 2
y = 0, x = −2, x = 2
None

Answer 1

The graph of the piecewise function has asymptotes at y = 0 and x = -2, x = 2.

The graph of the piecewise function has three pieces. In the first piece, the curve is increasing from the left through (-3, -5) and reaches a closed endpoint at (-2, 0). In the second piece, the function is linear with open endpoints at (-2, 1) and (2, -1). In the third piece, the curve starts at (2, 0), passes through (3, 5), and continues to increase to the right.

To determine the asymptote(s) of the function, we need to look at the behavior of the function as x approaches certain values. In this case, there is an asymptote at y = 0, because the function approaches but never touches the x-axis. There are also vertical asymptotes at x = -2 and x = 2, as the function approaches but never touches these vertical lines.

Therefore, the correct answer is: y = 0, x = -2, x = 2.