Question

Consider f(x)=x^2-4 g(x)=2f(x) h(x)=f(2x)

a) find g(x) and h(x) in terms of x
b) graph f(x) g(x) and h(x) on the same set of axes
c) describe fully the single transformation which maps the graph of f(x) onto graph of g(x)

Answer 1

a)

g(x) = 2f(x) = 2( x^2 - 4 ) = 2x^2 - 8

h(x) = f(2x) = (2x)^2 - 4 = 4x^2 - 4

c)

The transformation is a vertical stretch by a factor of 2. This means that every y-coordinate of f(x) is multiplied by 2 to obtain the corresponding y-coordinate of g(x). The x-coordinates remain unchanged. This transformation results in the stretching of the parabola in the y-direction, making it twice as tall.