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QuestionWhat is the new equation for the function after stretching f(x)=2xf(x)=2^{x} vertically by a factor of 3? A. g(x)=2⋅3xg(x)=2 \cdot 3^{x} B. g(x)=3⋅2xg(x)=3 \cdot 2^{x} C. g(x)=23xg(x)=2^{3 x} D. g(x)=13⋅2xg(x)=\frac{1}{3} \cdot 2^{x}

Studdy Solution

STEP 1

Assumptions1. The original function is f(x)=xf(x)=^{x} . The function is vertically stretched by a factor of3

STEP 2

A vertical stretch of a function by a factor of kk is represented by multiplying the function by kk. So, if we stretch the function f(x)=2xf(x)=2^{x} by a factor of, the new function g(x)g(x) will beg(x)=⋅f(x)g(x) = \cdot f(x)

STEP 3

Substitute f(x)=2xf(x)=2^{x} into the equation to get the new function g(x)g(x).
g(x)=3⋅2xg(x) =3 \cdot2^{x}So, the correct answer is B. g(x)=3⋅2xg(x)=3 \cdot2^{x}.

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