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Composition and transformations of functions

1.

f(x) = 7x + 7, g(x) = 6x2

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

42x2 + 42x
6x2 + 7x + 7
42x + 42
42x3 + 42x2

 

 

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.

and  (4 points)

Reflect the graph of f across the y-axis.
Reflect the graph of f across the y-axis and then reflect across the x-axis.
Reflect the graph of f across the x-axis.
The graph shifts left two units.

 

 

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

 

Last Updated on February 11, 2019

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