Question

The graph of the parent function f(x) = x3 is translated to form the graph of g(x) = (x + 3)3 – 4. The point (0, 0) on the graph of f(x) corresponds to which point on the graph of g(x)? (3, 4) (3, –4) (–3, 4) (–3, –4)

Answer 1

Answer:

(–3, –4)

Step-by-step explanation:

The parent function is

f(x) = x³.

The transformed function is

g(x) = (x+3)³-4.

Adding 3 to x before the exponent is applied will translate the function 3 units to the left.

Subtracting 4 from the end of the function will translate the function 4 units down.

This means the point (0, 0) will shift to (0-3, 0-4) = (-3, -4).

Answer 2

The new point will be equal to (–3, –4)

What is a parent function?

A parent function in mathematics is the simplest function in a family of functions that keeps the definition of the entire family.

The parent function is

f(x) = x³.

The transformed function is

g(x)   =   (  x  +  3  )³  -  4.

Adding 3 to x before the exponent is applied will translate the function 3 units to the left.

Subtracting 4 from the end of the function will translate the function 4 units down.

Therefore This means the point (0, 0) will shift to (0-3, 0-4) = (-3, -4).

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