Question

Label the points O(0, 0), A(-2, 4), and B(1, 1) on the graph
of f (x) x 2. Determine the images of these points on the transformed function. Label the images O',A' and B'

f(x)=1/2x^2+2

Answer 1

Label the points O(0, 0), A(-2, 4), and B(1, 1) on the graph

of f (x) = x²

transformation function

f(x) = $\frac{1}{2}$ x² +2

f(x) = $\frac{x^2}{2}$ + 2

f(0) = $\frac{0^2}{2}$ + 2 = 2

O' (0,2)

f(-2) = $\frac{(-2^2)}{2}$ + 2 = 4

A' ( -2,4)

f(1) = $\frac{1^2}{2}$ + 2 = $\frac{5}{2}$ = 2.5

B' (1,2.5)