# compositions and transformations of functions

Last Updated on 08/07/2021 by Sophia

1.

f(x) = 4x + 7, g(x) = 3x^{2}

Find (fg)(x). (4 points)

2.

Find (f + g)(x). (4 points)

3.

Describe how the graph of y = x^{2} can be transformed to the graph of the given equation.

y = (x – 10)^{2} + 8 (4 points)

4.

Describe how to transform the graph of f into the graph of g.

f(x) = x^{2} and g(x) = -(-x)^{2} (4 points)

5.

Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x).

f(x) = 4 cos x; g(x) = cos x (4 points)

6. A box is to be constructed from a sheet of cardboard that is 10 cm by 60 cm by cutting out squares of length x by x from each corner and bending up the sides. What is the maximum volume this box could have? (Round your answer to two decimal places.)