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) = 5(x - 9)^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).
select an answer

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

d) choose the correct transformation (vertical shifts).

Explanation:

Step1: Identify the parent function

$$f(x) = x^3$$

Step2: Identify reflections

There is no negative sign before the function or the variable \(x\), so there is no reflection.

Step3: Identify stretches or compressions

The factor of 5 multiplying the cubic term represents a vertical stretch by a factor of 5.

Step4: Identify vertical shifts

The constant term \(+4\) added to the function represents a vertical 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