Question

part 1 of 2
identify the transformation from the parent function $f(x)=0.25^{x}$. then graph the function.
$g(x)= -6(0.25)^{x+4}$

the graph of $f(x)$ is $\boldsymbol{□}$ vertically $\boldsymbol{□}$ by a factor of $\boldsymbol{□}$, and $\boldsymbol{□}$ $\boldsymbol{□}$ unit(s).
(type integers or decimals.)

Explanation:

Step1: Analyze vertical stretch/reflection

The coefficient $-6$ outside the parent function $f(x)=0.25^x$ first reflects the graph over the x-axis (due to the negative sign) and vertically stretches it by a factor of $6$.

Step2: Analyze horizontal shift

The exponent $x+4$ can be rewritten as $x-(-4)$. For exponential functions $f(x-h)$, a value of $h=-4$ means a shift left by 4 units.

Answer:

The graph of f(x) is reflected and stretched vertically by a factor of 6, and shifted left 4 unit(s).