Question

The graphs below have the same shape. What is the equation for the red graph?

Answer 1

Your answer would be B because even though it's the same shape the red shape is 2 times bigger.......your exponent 4 stays 4

Answer 2

Answer-

$\boxed{\boxed{g(x)=6-x^4}}$

Solution-

Here,

$f(x)=3-x^4$

As it is given that the graphs have the same shape, so it is neither stretched nor shrank i.e nothing is multiplied with x or y.

So, f(x) must have only translated, in order to get g(x).

As the g(x) is above f(x), so it must have been translated up.

The vertex of f(x) is at (0, 3) and vertex of g(x) is at (0, 6).

Hence, it is translated 3 units upward.

So,

$g(x)=f(x)+3$

$=3-x^4+3$

$=6-x^4$

Therefore, the equation of g(x) is $g(x)=6-x^4$