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How does the graph of g(x) = (x + 4)3 − 6 compare to the parent function f(x) = x3?
A. g(x) is shifted 6 units to the left and 4 units down.
B. g(x) is shifted 4 units to the right and 6 units down.
C. g(x) is shifted 6 units to the left and 4 units up.
D. g(x) is shifted 4 units to the left and 6 units down.

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Answer:

D

Step-by-step explanation:

f(x) = x³   (original function)

f(x) = x³ - 6    (shifted 6 units in the negative y direction - i.e 6 units down)

f(x) = (x+4)³ - 6

= [x- (-4) ]³ - 6 (shift 4 units in the negative x direction - i.e 4 units left)

adding up all the transformations, we get

4 units left and 6 units down (which corresponds to D)

A function assigns the value. The correct option is D, g(x) is shifted 4 units to the left and 6 units down.

How does the transformation of a function happen?

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

  • Left shift by c units, y=f(x+c) (same output, but c units earlier)
  • Right shift by c units, y=f(x-c)(same output, but c units late)

Vertical shift

  • Up by d units: y = f(x) + d
  • Down by d units: y = f(x) - d

Stretching:

  • Vertical stretch by a factor k: y = k × f(x)
  • Horizontal stretch by a factor k: y = f(x/k)

A function assigns the value of each element of one set to the other specific element of another set.

Given that the parent function is f(x)=x³, while the transformed function is g(x)=(x+4)³ - 6. Therefore, the transformation of the parent function that result in transformed function is that g(x) is shifted 4 units to the left and 6 units down.

Hence, the correct option is D, g(x) is shifted 4 units to the left and 6 units down.

Learn more about Transforming functions here:

https://brainly.com/question/17006186

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