What is the equation of the graph y=x^3 under a vertical stretch by the factor 2 followed by a horizontal translation 3 units to the left and then a vertical translation 4 units…

Question

What is the equation of the graph
`y=x^3` under a vertical stretch by the factor 2 followed by a horizontal translation 3 units to the left and then a vertical translation 4 units down?

a.)
`y=2(x+3)^3+4`
b.)
`y=2(x-3)^3+4`
c.)
`y=2(x+3)^3-4`
d.)
`y=2(x-3)^3-4`

Answer 1

C. y = 2 (x + 3)³ − 4

Explanation:

y = x³

Stretch vertically by 2.

y = 2x³

Shift horizontally 3 units to the left.

y = 2 (x + 3)³

Shift vertically 4 units down.

y = 2 (x + 3)³ − 4