compositions and transformations of functions

1.

f(x) = 4x + 7, g(x) = 3x2

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


2.

f as a function of x is equal to the square root of quantity 5 x plus 7, g as a function of x is equal to the square root of quantity 5 x minus 7

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



3.

Describe how the graph of y = x2 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) = x2 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.)