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

33

step-by-step explanation: g=6

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions