Question

Describe how to transform the graph of f into the graph of g. f(x) = x4 and g(x) = -(-x)4 Reflect the graph of f across the x-axis and then reflect across the y-axis. Shift the graph of f down 1 unit. Reflect the graph of f across the x-axis. Reflect the graph of f across the y-axis.

Answer 1

Answer: First option.

Step-by-step explanation:

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

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

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

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

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

In this case the exercise provides you the following parent function:

$f(x)=x^4$

And the function g(x):

$g(x) = -(-x)^4$

Knowing that the graph of the function $g(x)$ is the graph of the function $f(x)$ transformed, you can identify that the transformations is:

$g(x)=-f(-x)$

Therefore, based on the transformations explained at the beginning, to transform the graph of $f(x)$ to the graph of $g(x)$ you must: Reflect the graph of $f(x)$ across the x-axis and then reflect it across the y-axis.