# compositions and transformations of functions

1.

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

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

 12x2 + 21x 3x2 + 4x + 7 12x3 + 21x2 12x + 21

2. Find (f + g)(x). (4 points)   5x

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)

 Shift the graph of y = x2 left 10 units and then down 8 units. Shift the graph of y = x2 up 10 units and then right 8 units. Shift the graph of y = x2 left 10 units and then up 8 units. Shift the graph of y = x2 right 10 units and then up 8 units.

4.

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

f(x) = x2 and g(x) = -(-x)2 (4 points)

 The graph shifts left one unit. Reflect the graph of f across the y-axis and then reflect across the x-axis. Reflect the graph of f across the y-axis. The graph shifts down one unit.

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)

 Vertical stretch by a factor of 4 Horizontal stretch by a factor of 4 Vertical shrink by a factor of Horizontal shrink by a factor of 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.)