Question

Which of the following describes the transformations of g (x) = negative (2) Superscript x + 4 Baseline minus 2 from the parent function f (x) = 2 Superscript x?
shift 4 units left, reflect over the x-axis, shift 2 units down
shift 4 units left, reflect over the y-axis, shift 2 units down
shift 4 units right, reflect over the x-axis, shift 2 units down
shift 4 units right, reflect over the y-axis, shift 2 units down

Answer 1

Answer: First option.

Step-by-step explanation:

Below are some transformations for a function $f(x)$:

1. If $f(x)+k$, the function is shifted "k" units up.

2 If $f(x)-k$, the function is shifted "k" units down.

3. If $f(x-k)$, the function is shifted "k" units right.

4. If $f(x+k)$, the function is shifted "k" units left.

5. If $-f(x)$, the function is reflected over the x-axis.

6. If $f(-x)$, the function is reflected over the y-axis.

Then, given the parent function $f(x)$:

$f(x)=2^x$

And knowing that the the other function is:

$g(x)=-2^{(x+4)}-2$

You can identify that the function $g(x)$ is obtained by:

- Shifting the function $f(x)$ 4 units left.

-  Reflecting the function  $f(x)$ 4 over the x-axis.

- Shifting the function $f(x)$ 2 units down.