Question

in the above graph complete the following end behavior

$as x\to -infty, f(x)=\to$

$as x\to infty, f(x)=\to$

a) $-infty$

$infty$

c) $infty$

$infty$

b) $infty$

$-infty$

d) $-infty$

$infty$

Explanation:

Step1: Analyze \( x \to -\infty \)

Observe the left - most part of the graph. As \( x \) values become very large in the negative direction ( \( x \to -\infty \) ), the graph of the function is rising upwards, which means \( f(x) \to \infty \).

Step2: Analyze \( x \to \infty \)

Observe the right - most part of the graph. As \( x \) values become very large in the positive direction ( \( x \to \infty \) ), the graph of the function is rising upwards, which means \( f(x) \to \infty \).

Answer:

For \( \text{as } x\to-\infty, f(x)\to\infty \) and \( \text{as } x\to\infty, f(x)\to\infty \), the correct option is c) (where the first and second values are \( \infty \) and \( \infty \) respectively). So the answer is c) \( \infty \) (for \( x\to-\infty \)) and \( \infty \) (for \( x\to\infty \)) or in the option format: c) \( \infty \) \( \infty \)