Question

let $f(x) = 3^x$. which function represents a transformation of $f(x)$ by a vertical stretch with factor 6? $\bigcirc\\ g(x) = \frac{1}{6} \cdot 3^x$ $\bigcirc\\ g(x) = 3^{\frac{1}{6}x}$ $\bigcirc\\ g(x) = 3^{6x}$ $\bigcirc\\ g(x) = 6 \cdot 3^x$

Explanation:

Step1: Recall vertical stretch rule

For a function \( y = f(x) \), a vertical stretch by factor \( a \) (where \( a>1 \)) is given by \( y = a \cdot f(x) \).

Step2: Apply to \( f(x)=3^x \)

Here, the vertical stretch factor is 6. So we multiply \( f(x) \) by 6. Thus, \( g(x)=6\cdot 3^x \).

Answer:

\( g(x) = 6 \cdot 3^x \) (the last option among the given choices)