Question

The graphs below have the same shape.what is the equation of the red graph?

Answer 1

`G(x)=4-x^(4)`

Explanation:

Notice that the red graph is the blue graph shifted 1 units up.

According to the function transformation rules, we add
`k` to the output of the function to shift its graph
`k` units up, and we subtract
`k` to the output of the function to shift its graph
`k` units down.

The output of our function is
`3-x^(4)`, and since we want to shift 1 units up,
`k=1`. In other words, we just need to add 1 to the output of the function:

`G(X)=3-x^(4) +1`

`G(x)=3+1-x^(4)`

`G(x)=4-x^(4)`

We can conclude that the equation of the red graph is
`G(x)=4-x^(4)`.