Question

$f(x)=0.5^{x}$, $g(x)=6(0.5)^{x+5}-2$
the graph of $g$ is a $square$ by a factor of $square$, followed by a translation $square$ units left and 2 units $square$ of the graph of $f$.
options:
2, 4, 5, 6
up, down, left, right
vertical shrink, vertical stretch, horizontal shrink, horizontal stretch

Explanation:

Step1: Identify vertical transformation

For $f(x)=0.5^x$, $6\cdot f(x)$ is a vertical stretch by factor 6.

Step2: Identify horizontal translation

$6\cdot 0.5^{x+5}=6\cdot f(x+5)$ shifts left 5 units.

Step3: Identify vertical translation

$6\cdot 0.5^{x+5}-2$ shifts down 2 units.

Answer:

The graph of $g$ is a vertical stretch by a factor of $\boldsymbol{6}$, followed by a translation $\boldsymbol{5}$ units left and 2 units $\boldsymbol{down}$ of the graph of $f$.

Filled blanks:

1. vertical stretch
2. 6
3. 5
4. down