Question

The parent square root function of f(x) = √(x) is transformed into the function h(x) = 1/5 √(x - 8) + 4. Which of the following statements is true about the relationship between the function f(x) and the function h(x)?

a) The graph of h(x) is compressed by a factor of 5.

b) The graph of h(x) is shifted down 8 units.

c) The graph of h(x) is shifted left 8 units.

d) The graph of h(x) is stretched by a factor of 5.

e) The graph of h(x) is shifted right 4 units.

f) The graph of h(x) is compressed by a factor of 8.

g) The graph of h(x) is reflected over the x-axis.

Answer 1

The function h(x) is transformed from the parent function f(x) by shifting right by 8 units, being vertically compressed by a factor of 5, and shifting upwards by 4 units.

Step-by-step explanation:

The transformation of the parent square root function f(x) = √(x) into h(x) = 1/5 √(x - 8) + 4 consists of several steps. The function h(x) is first transformed by a horizontal shift right of 8 units due to the subtraction of 8 within the square root. This addresses the change from x to (x - 8). Next, the function is compressed vertically by a factor of 5, because of the multiplication of the square root function by 1/5. Additionally, there is a vertical shift upwards of 4 units, signified by the addition of 4 outside of the square root.

The specific statements about the function h(x) in the question are therefore:

• The graph of h(x) is compressed by a factor of 5 (True).
• The graph of h(x) is shifted to the right by 8 units (True).
• The graph of h(x) is shifted upwards by 4 units (True).

Therefore, the correct statements regarding the relationship between f(x) and h(x) are that h(x) experiences a horizontal shift right by 8 units, a vertical compression by a factor of 5, and a vertical shift up by 4 units.