Algebra test

Test 2 Written Portion Name:

This portion of the exam is worth 50% of your first exam. You must show all work to receive credit

and leave all answers exact unless otherwise specified. When you are done scan all pages into a single

PDF and upload to the corresponding Dropbox on FOLIO. Make sure to double check your file to

make sure all work is legible, in order, and the correct orientation. Work that is not legible will be

graded as incorrect and there will be a 5 point deduction for work that is not properly uploaded.

Problem 1. Graph the piecewise-defined function below. Label at least four points with

integer coordinates. (5 points)

1, 5 ( )

4, 5

x x g x

x

    

 

Problem 2. Determine the inverse function of 1 3

( ) 2

x g x

x

 

 . (7 points)

Problem 3. Determine the domain of 2

3 ( )

64

x R x

x

  

 . Write domain in interval notation. (5

points)

Problem 4. Let 2

( ) 3

x f x

x

 

 and

5 ( )

3 g x

x 

 . Evaluate. (5 points)

4) ( ) g

x f

     

Problem 5. Determine the average rate of change of 1

( ) 3

x g x

x

 

 from 0x  to x h . (7

points)

Problem 6. Use the graph of ( )f x below to graph the described transformation. (4 points)

( )f x ( 2) 3f x  

Problem 7. Test for Symmetry: 4 4 2 2

8x y x y  (3 points)

Problems 8-9. Provide the requested info. (14 points total)

8)

Function? ____________ Domain: ____________ Range: ____________

9)

Function? __________ One-to-One? ____________ Domain: ____________

Range: ____________ f(-0.38)=____________ x-intercept(s):__________

Where is f increasing? Use interval notation.

Where is f decreasing? Use interval notation.

Local minimums: ___________________

Local maximums: ___________________

Are there any absolute extrema? If so, describe.