Review for Module 1 Test

ONLINE MATH 1050 - College Algebra

MODULE 1 TEST

• There are 17 problems on this test

• You have 120 minutes to complete the test. Time starts once you access the test.

• This is an exam. Be academically honest! No notes, no • This is an exam. Be academically honest! No notes, no books, no websites, no helps of any kind.

• You will need to use your graphing calculator on some of the problems. Remember no calculators with CAS.

• Do not have ANY other windows open on your computer – they tend to “freeze” the exam.

6 3 7 8 0

Find the real solutions of the equation.

− − =x x

Problem #1

( ) ( )2

Find the real solutions of the equation.

4 x+1 11 1 6 0+ + + =x

Problem #2

2 1

3 3

Find the real solutions of the equation.

x 3 10 0− − =x

Problem #3

Problem #4Draw a complete graph so that it is symmetric with respect to the origin.

Problem #5

2

List the intercepts and type(s) of symmetry, if any.

9= +y x

Problem #6

2

Determine whether the graph of the equation is symmetric

with respect to the -axis, the -axis, and/or the origin.

1 0+ − =

x y

x y

Problem #72 8Find (2) when ( ) .

3

−=

+

xf f x

x

Problem #8

Find ( 9) when ( ) 6.− = −f f x x

Problem #9Find the domain of the function.

( ) 8 6= +f x x

Problem #10

2

Find the domain of the function.

( )12

=+

xf x

x

Problem #11Find the domain of the function.

( ) 10= −f x x

Problem #12For the given functions and , find the requested function and

state its domain.

( ) 6 3; ( ) 8 4

Find .

= − = −

−

f g

f x x g x x

f g

Problem #13For the given functions and , find the requested function and

state its domain.

( ) 5 1; ( ) 3 2

Find .

= + = −

f g

f x x g x x

f

g

Problem #14Use the graph of the function to find its domain and range,

the intercepts (if any), and any symmetry with respect to

the -axis, the -axis, or the origin.x y

Problem #15

Is this the graph of a function?

Problems #16 and#17

17) For what numbers is ( ) 0?=x f x

Problems #18 and#19

19) What is the domain of ?f

Problems #20 and#21

21) What is the -intercept?y

Problem #22

Problem #23The graph of a function is given. Decide whether it is

even, odd, or neither. Justify your response.

Problem #24The graph of a function is given. Decide whether it is

even, odd, or neither. Justify your response.

Problem #25The graph of a function is given. Decide whether it is

even, odd, or neither. Justify your response.

Problem #26

3

Determine algebraically whether the function

is even, odd, or neither.

( ) 5 3= −f x x

Problem #27

3

Determine algebraically whether the function

is even, odd, or neither.

( ) 4=f x x

Problem #28

4 2

Determine algebraically whether the function

is even, odd, or neither.

( ) 5= − −f x x x

Problem #29

( )

The graph of a function is given. Is this function

increasing. decreasing, or constant on the interval 1,2 ?

Problem #30Use the graph to find the numbers, if any,

at which has a local maximum. What are

the local maxima? Report your answers as

ordered pairs.

f

Problem #31

Find the function that is finally graphed after the following

transformations are applied to the graph of .

The graph is shifted down 6 units,

reflected about the -axis,

=y x

y

and finally shifted right 2 units.

Problem #32

( )Suppose the point 2,4 is on the graph of ( ).

Find a point on the reflection of the graph of

( ) across the -axis.

=

=

y f x

y f x x

Problem #33From a 10-inch by 10-inch piece of metal, squares are cut out of the four

corners so that the sides can then be folded up to make a box. Let represent

the length of the sides of the squares, in inche

x

s, that are cut out. Express the

volume of the box as a function of .x

FINAL WORDS OF ADVICE

• Write and work each problem in a notebook.

• Do a “memory dump” of any important equations or information you’ll need right after you start need right after you start your test

• Double-check each problem before submitting the test

• Relax and best of luck!