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QuestionWhich function has a horizontal asymptote at 4? A. f(x)=2(3)x+4f(x)=2(3)^{x}+4 B. f(x)=2x−4f(x)=2 x-4 C. f(x)=3(2)x−4f(x)=3(2)^{x}-4 D. f(x)=−3x+4f(x)=-3 x+4

Studdy Solution

STEP 1

Assumptions1. A horizontal asymptote is a line that the graph of a function approaches as x tends to infinity or negative infinity. . For a function of the form f(x)=a⋅bx+cf(x) = a \cdot b^x + c, the horizontal asymptote is at y = c.
3. For a function of the form f(x)=ax+bf(x) = ax + b, there is no horizontal asymptote.
4. We are looking for a function with a horizontal asymptote at y =4.

STEP 2

Let's analyze each optionA. f(x)=2()x+4f(x)=2()^{x}+4
The function is of the form f(x)=a⋅bx+cf(x) = a \cdot b^x + c. Here, c =4, so the horizontal asymptote is at y =4.
B. f(x)=2x−4f(x)=2x-4
The function is of the form f(x)=ax+bf(x) = ax + b. There is no horizontal asymptote for this function.
C. f(x)=(2)x−4f(x)=(2)^{x}-4
The function is of the form f(x)=a⋅bx+cf(x) = a \cdot b^x + c. Here, c = -4, so the horizontal asymptote is at y = -4.
. f(x)=−x+4f(x)=-x+4
The function is of the form f(x)=ax+bf(x) = ax + b. There is no horizontal asymptote for this function.

STEP 3

From the analysis in2, we can see that the correct answer is A. f(x)=2(3)x+f(x)=2(3)^{x}+, as it is the only function with a horizontal asymptote at y =.
The correct answer is A. f(x)=2(3)x+f(x)=2(3)^{x}+.

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