Question

determine the parent function from which the graph of the function shown below can be obtained. next, identify each transformation that can be applied to the parent function in order to obtain the graph of the function shown below.

(g(x) = \frac{1}{4}\sqrt{x-2}+1)

a) choose the correct parent function.

• (y = x^2)
• (y = x^3)
• (y = |x|)
• (y = \sqrt{x})
• (y = \sqrt3{x})

b) choose the correct transformation (reflections).
select an answer

c) choose the correct transformation (stretches/compressions).
select an answer

Explanation:

Step1: Identify the parent function

$$y = \sqrt{x}$$

Step2: Determine the reflection transformation

$$\text{No reflection}$$

Step3: Determine the stretch or compression

$$\text{Vertical compression by a factor of } \frac{1}{4}$$

Answer:

a) \(y = \sqrt{x}\)
b) No reflection
c) Vertical compression by a factor of \(\frac{1}{4}\)