Question

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

Answer 1

Answer:

$G(x)=4-x^{4}$

Step-by-step 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 $G(x)=4-x^{4}$.