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.

(f(x) = 5(x - 6)^3 + 4)

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).

c) choose the correct transformation (stretches/compressions).

d) choose the correct transformation (vertical shifts).

Explanation:

Step1: Identify the parent function

$$y = x^3$$

Step2: Determine the reflection transformation

$$\text{No reflection}$$

Step3: Determine the stretch/compression transformation

$$\text{Stretch vertically by a factor of 5}$$

Step4: Determine the vertical shift transformation

$$\text{Shift upward by 4 units}$$

Answer:

a) \(y = x^3\)
b) No reflection
c) Stretch vertically by a factor of 5
d) Shift upward by 4 units