Answer:
[tex]G(x)=4-x^{4}[/tex]
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 [tex]k[/tex] to the output of the function to shift its graph [tex]k[/tex] units up, and we subtract [tex]k[/tex] to the output of the function to shift its graph [tex]k[/tex] units down.
The output of our function is [tex]3-x^{4}[/tex], and since we want to shift 1 units up, [tex]k=1[/tex]. In other words, we just need to add 1 to the output of the function:
[tex]G(X)=3-x^{4} +1[/tex]
[tex]G(x)=3+1-x^{4}[/tex]
[tex]G(x)=4-x^{4}[/tex]
We can conclude that the equation of the red graph is [tex]G(x)=4-x^{4}[/tex].
