A rational function is graphed on the coordinate plane.The graph consists of three curves. The first curve starts just above y = 2 and increases, approaching but never reaching x = negative 2. The second curve starts at the bottom of the graph just to the right of x = negative 2 and increases until just below y = 2, then decreases, approaching but never reaching x = 2. The third curve starts at the top of the graph just to the right of x = 2 and decreases down and to the right approaching but never reaching y = 2. There are arrows on both ends of each curve.

Question

Question
Use the graph to answer the question.
Identify all of the asymptotes for the graphed function. Select all that apply.
(2 points)
Responses

x = 2
x = 2

x = 0
x = 0

x equals negative 2
Image with alt text: x equals negative 2

y = 2
y = 2

y = 0
y = 0

y equals negative 2

Answer 1

Based on your description of the graph of the rational function, we can identify the asymptotes as follows:

1. Vertical asymptotes: These occur where the function approaches but never reaches a specific x-value. According to the description, the graph has vertical asymptotes at:

   • x = -2 (since the first curve approaches but never reaches x = -2)
   • x = 2 (since the second curve approaches but never reaches x = 2)

2. Horizontal asymptote: This occurs when the function approaches a specific y-value as x approaches infinity or negative infinity. Your description indicates that the function approaches y = 2 (the value it gets closer to, but never reaches) from both sides:

   • y = 2

Based on this analysis, the asymptotes for the graph are:

• \( x = -2 \)
• \( x = 2 \)
• \( y = 2 \)

Therefore, the correct responses are:

• \( x = -2 \)
• \( x = 2 \)
• \( y = 2 \)