Question

look at the graph:
what are the equations of the horizontal and vertical asymptotes?
horizontal asymptote:
vertical asymptote:

Explanation:

Step1: Analyze Horizontal Asymptote

A horizontal asymptote is a horizontal line that the graph approaches as \( x \to \pm\infty \). From the graph, as \( x \) becomes very large (positive or negative), the \( y \)-values approach 5. So the horizontal asymptote is \( y = 5 \).

Step2: Analyze Vertical Asymptote

A vertical asymptote is a vertical line that the graph approaches as \( x \) approaches a certain value. From the graph, the graph has a vertical break at \( x = 0 \) (the y - axis), and the graph approaches this line as \( x \) approaches 0. So the vertical asymptote is \( x = 0 \).

Answer:

horizontal asymptote: \( y = 5 \)
vertical asymptote: \( x = 0 \)