Question

Which describes how to graph h(x) = -√x + 8 by transforming the parent function?

O Reflect the parent function over the y-axis, and translate it 3 units to the right.
O Reflect the parent function over the y-axis, and translate it 3 units to the left.
O Reflect the parent function over the x-axis, and translate it 8 units to the right.
O Reflect the parent function over the x-axis, and translate it 8 units to the left.

Answer 1

The correct answer is: Reflect the parent function over the x-axis, and translate it 8 units up.

The parent function of h(x) is the square root function f(x) = √x. The transformation of h(x) includes a reflection over the x-axis, a vertical shift 8 units up, and a reflection over the y-axis. The order of these transformations matters, so we can simplify the process by reversing the order and applying the transformations one by one.

First, reflect the parent function over the y-axis:

g(x) = -f(x) = -√x

Next, shift the graph 8 units up:

h(x) = g(x) + 8 = -√x + 8

Therefore, the answer is: Reflect the parent function over the x-axis, and translate it 8 units up.

Step-by-step explanation: yes