Question

Given that f(x) = x^2 .Type a function that would shift f(x) up 7 units, vertically stretch the function by a factor of 9, and reflect is across the y-axis?

Answer 1

Given that f(x) = x^2

vertically stretch the function by a factor of 9

For vertical stretch we multiply the factor by f(x)

`f(x) = x^2`

for vertical stretch ,
`f(x) = 9f(x)= 9x^2`

reflect is across the y-axis

While reflect across y axis , f(x) becomes f(-x). we replace x with -x

`f(x)= 9x^2` becomes
`f(x)= 9(-x)^2`

shift f(x) up 7 units

when shifting f(x) up by 7 units we add 7 at the end of f(x)

`f(x)= 9(-x)^2` becomes
`f(x)= 9(-x)^2 + 7`

So
`f(x)= 9(-x)^2 + 7`