MATH 151 MCC Mathematics Algebra Worksheet

MAT 151Final Sp 2020
St. Amand
Name__________________________
Date___________________________
Please show all work for complete credit.
1.
Given the following piece-wise defined function:
− x 2
− 2  x 1

f ( x) = − 2 x − 7
3 x5
3
7  x  10

a) Find f (1) ______________
d) domain (interval notation)___________
7
 _____________
2
b) Find f 
c) Find f (8) ______________
e) range (interval notation)____________
d) Sketch f (x )
College Algebra
L. St. Amand
Final
Sp 2019
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2. The graph of g (x ) is given below.
Find the corresponding points that lie on the graph of
2g (x − 2) − 2 and sketch its graph on the same set of axes as g (x ) .
g (x )
(-2,0) becomes______________
(0,2) becomes_______________
(2,-1) becomes_______________
(4,0) becomes________________
3. Tell if the function f ( x ) =
x2 + 2
− x3
is even, odd or neither. Show your ‘test’ for complete credit.
3. __________________________
College Algebra
L. St. Amand
Final
Sp 2019
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4. Given
f (x ) = − x 2 − 2 x + 1. Find the difference quotient
f (x + h ) − f (x )
.
h
4. __________________________
5. Find the complex zeroes for each of the following. Use the method you feel is best, unless
otherwise noted. Write your answer as a solution set { } on the line for each problem.
a. 2( x − 3) + 5 = 1
2
a.
College Algebra
L. St. Amand
Final
Sp 2019
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3


b. 5 x( x − 3) = −4 3 x −
1

2
b. _____________________
a.
0 = 5x + 13 x − 6 use u-substitution. Define u
c.______________________
6. Solve − 2( x − 2 ) ( x + 4 )( x + 2 )  0 give your answer in interval notation.
2
3
6. _____________________
College Algebra
L. St. Amand
Final
Sp 2019
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7. Use the remainder theorem to find
f (2) for f (x ) = x 2 + x − 6
7. ______________________
8. Provide the requested information for the function below
y = log 2 (x + 1) − 3
Domain:_____________________
Range:______________________
Asymptote equation:____________
Intercept(s):__________________
x-y chart:
College Algebra
L. St. Amand
Final
Sp 2019
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9. Find the inverse of the function f ( x ) =
2x + 4
using the 4 step method
3 − 7x
9.__________________________
10. Solve for x: 5
x−2
= 4x .
Exact______________________
Approx.____________________
College Algebra
L. St. Amand
Final
Sp 2019
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 − 4x + 3 
 + 1. Give the answer in interval notation.
 3 − 2x 
11. Find the domain of y = log 
11.________________________
12. Solve using a matrix. You must clearly indicate your row operations. Do not just plug into a
calculator
𝑥+𝑦−𝑧 = 6
{ 3𝑥 − 2𝑦 + 𝑧 = −5
𝑥 + 3𝑦 − 2𝑧 = 14
College Algebra
L. St. Amand
Final
Sp 2019
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12._____________________
x − x −8
(x + 1)(x 2 + 5x + 6)
2
13. Find the partial fraction decomposition of
13.__________________________
14. Solve the system :
x 2 − y 2 = 21
using substitution
x+y=7
14.__________________________
College Algebra
L. St. Amand
Final
Sp 2019
8