Question

what is the end behavior for the following graph of a function:
graph of a function on a coordinate plane
select one or more:
□ a. $f(x) \to \infty$ as $x \to -\infty$
□ b. $f(x) \to \infty$ as $x \to \infty$
□ c. $f(x) \to -\infty$ as $x \to -\infty$
□ d. $f(x) \to -\infty$ as $x \to \infty$
□ e. cannot tell just from the graph

Explanation:

Step1: Analyze left end behavior

Look at the graph as \( x \to -\infty \) (left side). The left end of the graph is going up (towards positive infinity). So \( f(x) \to \infty \) as \( x \to -\infty \).

Step2: Analyze right end behavior

Look at the graph as \( x \to \infty \) (right side). The right end of the graph is going up (towards positive infinity). So \( f(x) \to \infty \) as \( x \to \infty \).

Answer:

a. \( f(x) \to \infty \) as \( x \to -\infty \)
b. \( f(x) \to \infty \) as \( x \to \infty \)