What is the equation of y = x^3 with the given transformations? vertical stretch by a factor of 3, horizontal shift 4 units to the right, vertical shift 3 units down. step-by-step process i really need to understand

y = 3(x - 4)^3 - 3

Step-by-step explanation:

A vertical stretch factor 3 is given by 3x^3.  Horizontal shift 4 to the right is given by 3(x - 4)^3. Finally we  add -3 to this function to move it 3 units down.

Answer is y = 3(x- 4)^3 - 3

Question:

What is the equation of y = x 3 with the given transformations? vertical stretch by a factor of 3, horizontal shift 4 units to the right, vertical shift 3 units down.

Answers:

(1) y = 3(x - 4)³ - 3

(2) y = 3(x - 4)^3 - 3

Step-by-step explanations:

(1) The parent function is y = x³.

After a vertical stretch by a factor of 3, obtain

y = 3x³

After a horizontal shift 4 unit to the right, obtain

y = 3(x - 4)³

After a vertical shift 3 units down, obtain

y = 3(x - 4)³ - 3

(2) A vertical stretch factor 3 is given by 3x^3.  Horizontal shift 4 to the right is given by 3(x - 4)^3. Finally we  add -3 to this function to move it 3 units down.

Answer is y = 3(x- 4)^3 - 3