Question

If y = f(x), and y = af(x) is a vertical stretch or compression, a > 1 causes the graph to be stretched vertically by a factor of a.

False? Yes?

Answer 1

let's just use y = f(x) = x^2... use your previous problem as an example to see what's going on. And pick an "a" so that a > 1... let's choose a = 3.

Answer 2

so if y = x^2

then a different y is = ax^2.... and we said "a = 3", so this stretched y is = 3x^2

So, with normal y = x^2, when x = 1, y = 1, and when x = 2, y = 4

With the stretched y = 3x^2, when x = 1, y = 3(1)^2 = 3 and for x = 2, y = 3(2)^2 = 12

So the curve stretches higher on the y axis when you have an "a" in front of the function... it multiplies all the old y values by 3, stretching them.

Answer 3

so then it would be true?