Question

What is the equation of y = x³ with the given transformations?

vertical stretch by a factor of 3, horizontal shift 4 units to the right, vertical shift 3 units down

Answer 1

The equation of y = 2³ with the described transformations is y =
`3(x- 4)^3 - 3.`

The original equation is
`y = x^3` . Let's apply the he given transformations step by step.

1. Vertical stretch by a factor of 3: This means multiplying the entire function by 3. The equation becomes
`y = 3x^3`.

2. Horizontal shift 4 units to the right: To shift a function to the right, you replace with (xh), where h is the amount of shift. So, shifting 4 units to the right means replacing 2 with (x - 4). The equation becomes
`y = 3(x - 4)^3`.

3. Vertical shift 3 units down: To shift a function down, you subtract the amount from the function. So, shifting 3 units down means subtracting 3 from the entire function. The equation becomes
`y = 3(x - 4)3^3.`

Therefore, the equation of y = 2³ with the described transformations is y =
`3(x- 4)^3 - 3.`