Problema Solution
Determine the value for ‘a’ and ‘b’ resulting in a vertical stretch, af(x), being equivalent to a horizontal stretch, f(bx), for each of the base graphs, y = x2, y = √x, y = x3, y = 1/x.
Provide the general formula for each and one numerical example.
Answer provided by our tutors
af(x)= f(bx)
y = f(x)
For y = x^2
a*x^2 = (bx)^2
ax^2 = b^2x^2
a = b^2
For y = √x
a*√x = √bx
a = √b
For y = x^3
a*x^3 = (bx)^3
a = b^3
For y = 1/x
a*(1/x) = 1/(bx)
a = 1/b
The general formula is a = f(b).