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

f(x) = x^2

1st transpose: f(x) = x^2 +7

2nd dilate: f(x) = 9(x^2+7)

3rd reflect: f(x) = 9x^2 + 63

Answer 2

f(x) = x^2

shift f(x) up 7 units means adding 7 to f(x)

so now f(x) = x^2 +7

vertically stretch the function by a factor of 9 means multiplying f(x) by 9

so now f(x) = 9(x^2+7)

f(x) = 9x^2 + 63

reflect across the y-axis means x becomes -x in f(x)

so now f(x) = 9(-x)^2 + 63

f(x) = 9x^2 + 63