Question

Identify the transformations of the function from the parent function f(x) = x^4, g(x)=(14x)⁴+8.

A. Vertical stretch
B. Vertical compression
C. Horizontal stretch
D. Horizontal compression
E. Shift left
F. Shift right
G. Shift up
H. Shift down

Answer 1

The function g(x) has undergone a horizontal compression and a vertical shift upward from the parent function f(x) = x^4.

Step-by-step explanation:

Looking at the function g(x) = (14x)⁴ + 8 and comparing it to its parent function f(x) = x⁴, we can identify two transformations. The coefficient 14 in front of x indicates a horizontal compression by a factor of 1/14. This is because you would have to compress the x values by a factor of 1/14 to make them 14 times larger so that when raised to the fourth power, the function would match the new coefficient. The vertical shift is identified by the constant +8, which translates the entire function vertically upward in the coordinate system by 8 units. Therefore, the transformations are a horizontal compression and a vertical shift up.