Question

which statement describes the end behavior of the function f (x) = 1/7 | x - 4 | + 3?

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

Answer 1

Question:

What is the end behavior of this radical function?

$f\left(x\right)=3\sqrt[3]{x-4}$

1. As x approaches positive infinity, f(x) approaches positive infinity.

2. As x approaches negative infinity, f(x) approaches positive infinity.

3. As x approaches positive infinity, f(x) approaches negative infinity.

4. As x approaches negative infinity, f(x) approaches 0.

Answer:

1. As x approaches positive infinity, f(x) approaches positive infinity.

Explanation:

In photo below

Answer 2

Using limits, it is found that the statement which describes the end behavior of the function f(x) is:

B. As x approaches negative infinity, f(x) approaches positive infinity.

How we find the end behavior of a function f(x)?

It is given by the limit of f(x) as x approaches both positive infinity and negative infinity.

In this problem, the function is:

$f(x) = \frac{1}{7}|x - 4| + 3$

Hence, the limits are:

$\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} = \frac{1}{7}|x - 4| + 3 = \frac{1}{7}|-\infty - 4| + 3 = \infty$

$\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} = \frac{1}{7}|x - 4| + 3 = \frac{1}{7}|\infty - 4| + 3 = \infty$

Approaches positive infinity in both cases, hence option B is correct.

You can learn more about limits and end behavior at https://brainly.com/question/22026723