Question

When graphed, which function has a horizontal asymptote at 4?

Answer 1

Answer:

Correct answer: C. f(x) = 2(3)x + 4

(please note we changed the expression of the function to exponential form which we believe is the correct form of the question)

Step-by-step explanation:

Horizontal Asymptote

The graph of a function is said to have a horizontal asymptote at y=a if one or both the following limits exist

$\lim\limits_{x \rightarrow \infty}f(x)=a$

$\lim\limits_{x \rightarrow -\infty}f(x)=a$

The horizontal asymptotes are horizontal lines to which the function tends when x increases or decreases without limits.

Let's analyze each one of the options provided:

A.  f(x) = 2x -4

$\lim\limits_{x \rightarrow \infty}(2x-4)=+\infty$

$\lim\limits_{x \rightarrow -\infty}(2x-4)=-\infty$

No horizontal asymptote

B.  f(x) = -3x + 4

$\lim\limits_{x \rightarrow \infty}(-3x+4)=-\infty$

$\lim\limits_{x \rightarrow -\infty}(-3x+4)=\infty$

No horizontal asymptote

C. f(x) = 2\cdot 3^x + 4

$\lim\limits_{x \rightarrow \infty}(2\cdot 3^x + 4)=2\cdot 3^\infty + 4=\infty$

$\lim\limits_{x \rightarrow \infty}(2\cdot 3^x + 4)=2\cdot 3^{-\infty} + 4=0+4=4$

This function has a horizontal asymptote at y=4

D. 3\cdot 2^x -4

$\lim\limits_{x \rightarrow \infty}(3\cdot 2^x - 4)=3\cdot 2^\infty - 4=\infty$

$\lim\limits_{x \rightarrow \infty}(3\cdot 2^x- 4)=3\cdot 2^{-\infty} - 4=0-4=-4$

This function has a horizontal asymptote at y=-4

Correct answer: C.