PreCalculus Honors

Unit Test #1

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No Calculator Allowed

 

1.

Describe a sequence of transformations that will transform the graph of y= x 3 into the graph of y= x2 3 +3 .

(4)

Shift two units right and three units up.

 

2.

Describe a sequence of transformations that will transform the graph of y= 1 x into the graph of y= 2 x+3 .

(4)

Multiply the y-values by two and shift three units left.

 

3.

Sketch the graph of f x = x2 2 +3 . Label a few key points.

(5)

An Image

 

4.

Sketch the graph of g x =3 x2 . Label a few key points.

(5)

An Image

 

For all questions on this page, let f x = x 2 4 and g x =2x+5 .

 

5.

Find f+g x .

(4)

x 2 +2x+1

 

6.

Find f g x .

(4)

x 2 4 2x+5

 

7.

Find fg 3 .

(4)

3 2 4 23+5 =6

 

8.

Find fg 2 .

(4)

2 2 4 22+5 =0

 

9.

Find fg x .

(4)

2x+5 2 4=4 x 2 +20x+21

 

10.

Find gf x .

(4)

2 x 2 4 +5=2 x 2 3

 

11.

Find non-trivial functions f x and g x so that fg x = x 2 +3 .

(3)

How about f x = x and g x = x 2 +3 ?

 

12.

Are f x = x 3 and g x = x 5 2 inverse functions? Justify your answer.

(4)

They are not—when composed, they do not reduce to just x. g f x = x 3 5 2x .

 

13.

Find the inverse function of p x = 1 x+2 3 .

(5)

y= 1 x+2 3 …swap variables first. x= 1 y+2 3 . Now, solve for y: x+3= 1 y+2 y+2= 1 x+3 y= 1 x+3 2 . Thus, p 1 x = 1 x+3 2 .

 


Page last updated 14:23 2021-02-16