Question

what is the horizontal asymptote?
y=3
y=-100
y=2
y=0

Explanation:

Step1: Recall Horizontal Asymptote

A horizontal asymptote is a horizontal line \( y = k \) that a graph approaches as \( x \to \pm\infty \). For exponential functions (like the curve shown, likely an exponential growth/decay), if it's of the form \( y = a^x + c \) (or similar), the horizontal asymptote is \( y = c \).

Step2: Analyze the Graph

The graph shown is an exponential - like curve (increasing, approaching a horizontal line as \( x\to -\infty \)). Looking at the graph, as \( x \) becomes very negative, the curve approaches the \( x \) - axis (where \( y = 0 \)). The other options (\( y = 3\), \( y=- 100\), \( y = 2\)) do not match the behavior of the graph. The graph is approaching \( y = 0\) as \( x\to-\infty \).

Answer:

\( y = 0 \) (or the option "y = 0")