Question

Which of the following describes the transformation of g(x) = -(2)x+4 -2 from the parent function f(x)= 2^x

Answer 1

Answer:

Shift 4 units left, reflected over x-axis, shift two units down.

Step-by-step explanation:

We have been given formula of a parent function $f(x)=2^x$ and we are asked to find the transformations that are used to get $g(x)=-(2)^{x+4}-2$ from our given parent function.

Let us recall transformation rules.

$f(x-a)\rightarrow \text{Graph shifted to right by a units}$,

$f(x+a)\rightarrow \text{Graph shifted to left by a units}$,

$f(x)+a\rightarrow \text{Graph shifted upwards by a units}$,

$f(x)-a\rightarrow \text{Graph shifted downwards by a units}$,

$f(-x)\rightarrow \text{Graph reflected across y-axis}$,

$-f(x)\rightarrow \text{Graph reflected across x-axis}$.

Upon looking at our given f(x) and g(x),we can see these transformations:

• Our parent function is shifted to left by 4 units.
• Our parent function is reflected over x-axis.
• Our parent is shifted downwards by 2 units.

Therefore, option A is the correct choice.

Answer 2

Ok, so what happend was 4 was added to every x, the whole thing was multiplied by -1 and -2 was added to the whole function

so
adding 4 to every x shifts the graph to the left 4 units
multiplying the whole function by -1 reflects it over the x axis
adding -2 to the whole function moves it down2 units

so that would be the first option