Question

select the end behavior of the exponential function shown in the graph above.
a the graph goes from -8 to 2 on the x - axis and 0 to 8 on the y - axis.
b as x approaches 0, y approaches -∞. as x approaches ∞, y approaches ∞.
c as x approaches -∞, y approaches 0. as x approaches ∞, y approaches ∞.
d as x approaches -∞, y approaches -∞. as x approaches ∞, y approaches ∞.

Explanation:

Step1: Analyze the graph as \(x\to-\infty\)

As \(x\) approaches \(-\infty\), we look at the left - hand side of the graph. The graph gets closer and closer to the \(x\) - axis (\(y = 0\)). Mathematically, \(\lim_{x\to-\infty}f(x)=0\).

Step2: Analyze the graph as \(x\to+\infty\)

As \(x\) approaches \(+\infty\), we look at the right - hand side of the graph. The graph rises without bound. Mathematically, \(\lim_{x\to+\infty}f(x)=+\infty\).

Answer:

C. As \(x\) approaches \(-\infty\), \(y\) approaches \(0\). As \(x\) approaches \(\infty\), \(y\) approaches \(\infty\).