Question

If you horizontally shift the function below,

F(x)=x^ 4+4, left 4 units, what is the equation of the new function?

a)F(x)=(x+4) ^4+4

b) F(x)=(x−4) ^4+4

c)F(x)=x ^4−4

d) F(x)=x ^4+8

Answer 1

To horizontally shift the function F(x) = x^4 + 4 left by 4 units, replace x with (x + 4), resulting in the new equation F(x) = (x + 4)^4 + 4.

Step-by-step explanation:

To horizontally shift the function F(x) = x^4 + 4 left 4 units, we need to subtract 4 from the input variable, x. So the new equation will be:

F(x - 4) = (x - 4)^4 + 4

When you shift the function horizontally, it involves replacing the x variable in the equation with (x ± d), where d is the horizontal shift distance. A positive d shifts the function to the left, so for the function F(x) = x^4 + 4, shifting it to the left by 4 units replaces x with (x + 4).

The equation of the new function after shifting it horizontally left by 4 units is:

F(x) = (x + 4)^4 + 4