Question

What is the effect on the graph of f(x) = x^2 when it is transformed to h(x) = (1/8)x^2 - 13?

A. Horizontal compression and vertical translation downward
B. Vertical compression and horizontal translation to the left
C. Horizontal expansion and vertical translation upward
D. Vertical expansion and horizontal translation to the right

Answer 1

The graph of the function is horizontally compressed and vertically translated downward.

Step-by-step explanation:

The graph of the function f(x) = x^2 is a parabola that opens upward. When this function is transformed to h(x) = (1/8)x^2 - 13, the graph is horizontally compressed and vertically translated downward.

The horizontal compression is caused by the coefficient (1/8) in front of the x^2 term. The value of x is multiplied by 1/8, which makes the parabola narrower. The vertical translation downward is caused by the constant term -13, which shifts the entire graph downward by 13 units.