Give an example of a function whose graph is the graph of y

Question

Answer the following questions on a separate sheet of paper. Your answers must also be legible and show complete detail.

1. Given that f(x) = 5x² and g(x) =3x + 5, determine the following:
(a) (f + g)(x)
(b) (g - f)(x)
(c) (f . g)(x)
(d) (f o g)(x)

2. Given that f(x) = 4x² + 3x - 8 and g(x) = 3x² - 4x + 5, determine the following:
(a) (f . g)(x)
(b) (g o f)(x)

3. Determine functions f(x) and g(x) such that (f o g)(x) = h(x) if h(x) = (2x - 10)⁶.

4. Give an example of a function whose graph is the graph of y =x² shifted to the right 4 and down 3.

5. Sketch the graphs of y = x² and y = 0.5(x - 3)² + 1 on the same axis.

6. Determine an equation of variation for the following: y varies directly as the square of x, and y = 6 when x = 3.