Question

Which statement describes the end behavior of this function? g(x) = 1/2|x - 3| - 7

A. As x approaches positive infinity, g(x) approaches negative infinity.
B. As x approaches negative infinity, g(x) approaches negative infinity.
C. As x approaches positive infinity, g(x) approaches positive infinity.
D. As x approaches negative infinity, g(x) is no longer continuous.

Answer 1

C. As x approaches positive infinity, g(x) approaches positive infinity.

Explanation:

We are given the following function:

`g(x) = (|x-3|)/(2) - 7`

End behavior:

Limit of g(x) as x goes to negative and positive infinity.

Negative infinity:

`\lim_(x \rightarrow -\infty) g(x) = \lim_(x \rightarrow -\infty) (|x-3|)/(2) - 7 = (|-\infty-3|)/(2) - 7 = |-\infty| = \infty`

Positive infinity:

`\lim_(x \rightarrow \infty) g(x) = \lim_(x \rightarrow \infty) (|x-3|)/(2) - 7 = (|\infty-3|)/(2) - 7 = |\infty| = \infty`

So in both cases, it approaches positive infinity, and so the correct option is c.