Question

The function f(x) = x4 has been transformed, resulting in the functions below. Tell how you would create the new function from the old function.

A.H(x) = (x – 3)4 +7


B. M(x) = - (x + 7)4 – 10


C. S(x) = (-x)4 + 8

Answer 1

C I will be there for

Answer 2

To create the new functions from f(x) = x^4:

H(x): Shift right 3 units and up 7 units.

M(x): Shift left 7 units, reflect vertically, and down 10 units.

S(x): Reflect across the y-axis and up 8 units.

Step-by-step explanation:

Each function is a transformation of f(x) = x^4 achieved through various manipulations:

Horizontal shifts: Adding or subtracting a constant to x shifts the curve left or right.

Vertical shifts: Adding or subtracting a constant to the entire expression shifts the curve up or down.

Reflection: Multiplying by -1 reflects the curve across the y-axis.

By analyzing the differences between f(x) and each new function, we can identify the specific transformations applied. Therefore, the options that accurately describe these transformations are:

A. H(x): (x - 3)^4 + 7 (Right shift of 3, up shift of 7)

B. M(x): - (x + 7)^4 - 10 (Left shift of 7, reflection, down shift of 10)

C. S(x): (-x)^4 + 8 (Reflection, up shift of 8)

Remember, understanding the effects of these transformations is crucial for manipulating functions and creating desired variations.