Need help with my assignment in Math

Math

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) = 5x 2 and g(x) = 3x + 5, determine the following:

(a) (f + g)(x) (b) (g − f)(x)

(c) (f · g)(x) (d) (f ◦ g)(x)

2. Given that f(x) = 4x 2 + 3x − 8 and g(x) = 3x 2 − 4x + 5, determine the following:

(a) (f · g)(x) (b) (g ◦ f)(x)

3. Determine functions f(x) and g(x) such that (f ◦ g)(x) = h(x) if

h(x) = (2x − 10)6 .

4. Give an example of a function whose graph is the graph of y = x 2 shifted to the right 4 and down 3.

5. Sketch the graphs of y = x 2 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.