Unit 2 Homework Problems MAT150 College Algebra
© Andrew McKintosh 2010
All problems should be done WITHOUT a calculator unless otherwise indicated!!!!
Day 15 Homework: Topics: Solutions to equations, graphing equations, x & y intercepts, symmetry, circles.
Supplemental Reading:
1. http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut12_graph.htm
2. http://tutorial.math.lamar.edu/Classes/Alg/Symmetry.aspx
3. http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut29_circles.htm (ex 1 - 3 only)
1. Without graphing, determine whether or not the point  2,3 lies on the graph of each of the following equations.
A) 2x  3 y  5
B) y  x 2  1
2  2   3  3  5 ?
4  9  5 ?
13  5 NO !
C) y 2  x 2  13
3   2   1 ?
 3
3  4 1 ?
3  3 YES !
9  4  13 ?
5  13 NO !
2
2
  2   13 ?
2
2. Complete the table. Use the resulting solution points to graph the equation.
2
y   x4
3
x
0
y
4
(x , y)
(0,4)
3
2
(3,2)
-3
6
(-3,6)
3/2
3
(3/2,3)
-3/2
5
(-3/2,5)
B) y   x 2  4
x
y
(x , y)
1
3
(1,3)
-1
3
(-1,3)
2
0
(2,0)
-2
0
(-2,0)
A)
0
4
(0,4)
(Day 15 Homework continued)
© Andrew McKintosh 2010
3. Write down the X and Y Intercepts for each graph shown below. Be sure to write your answers as ORDERED
PAIRS NOT just single numbers.
1, 0 
X int =
 0, 1
Y int =
X int =
 2,0 3,0
Y int =
 0, 4
4. Use the algebraic tests for symmetry to check for symmetry with respect to the x-axis, y-axis and origin.
A) y  3 x 3  4 x
B) y  5 x 2  2 x 4  3
x  axis  y  3x 3  4 x
y  3x3  4 x
y  axis
y  5 x 2  2 x 4  3 NO
NO
y  x  4 x
3
y  3x3  4 x
origin
x  axis  y  5 x 2  2 x 4  3
y  axis
3
 y  3x3  4 x
y  3x3  4 x YES
2
4
y  5 x 2  2 x 4  3 YES
NO
 y  x  4x
y  5x  2 x  3
origin
 y  5x  2x  3
2
4
 y  5x2  2 x4  3
y  5 x 2  2 x 4  3 NO
5. Write the standard for m of the equation of a circle with……
A) Center  3, 2  and Radius = 5
 x  h   y  k   r 2
2
2
 x  3   y  5  52
2
2
 x  3   y  5  25
2
2
B) Endpoints of a diameter
 x  h
2
 2,5
and
  y  k   r2
2
2  4 5  3   2 2 
,
   ,   1,1
2  2 2
 2
 h, k   
 x  1   y  1  r 2
2
2
 2  1   5  1  r 2
2
2
 3   4   r 2
2
2
9  16  r 2
25  r 2
 x  1
2
  y  1  25
2
 4, 3
Day 16 Homework: Topics: Solving linear equations.
© Andrew McKintosh 2010
Supplemental Reading:
1. http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut14_lineareq.htm
1. Determine whether each of the following equations are conditional, a contradiction or an identity.
A) 2x  3x  4  5   x  2
B) 2x  3x  4  5   x  2
C) 2x  3x  4  5   x  9
2 x  3x  4  5  x  2
x  4  3  x
2 x  3x  4  5  x  2
x  4  7  x
4  3
contradiction
2 x  11
11
x
2
conditional
2 x  3x  4  5  x  9
 x  4  4  x
4  4
identity
2. Solve the following equations.
A)
1
1
1

 x  5  4 x  
3
2
4

B) .03x  1  2 .3  x 
.03 x  1  .6  2 x
1
1
1
x 5  4 x
3
6
4
1
1
1
12  x  12   12  5  12  4  12  x  12 
3
6
4
4 x  2  60  48  12 x  3
4 x  62  45  12 x
16 x  107
107
x
16
100  .03x  1100   .6 100   100  2 x
3 x  100  60  200 x
203 x  160
x
160
203
C) 2x  3 5  x   9  5  x  6
2 x  15  3x  9  5 x  30
5 x  15  5 x  21
15  21
No Solution
3. Find the x and y intercepts algebraically
2x  3 y  12
4. Solve the following equation.
1
1
10

 2
x 3 x 3 x 9
2 x  12
1
1
10


x  3 x  3  x  3 x  3
x  6
 x  3 x  3 
x  int : let y  0
 6, 0 
y  int : let x  0
3 y  12
y4
 0, 4 
1
1
10
  x  3 x  3 
  x  3 x  3 
 x  3
 x  3
 x  3 x  3
x  3  x  3  10
2 x  10
x5
Day 17 Homework: Topics: Word Problems that lead to Linear Equations
© Andrew McKintosh 2010
Supplemental Reading:
1. http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut16_prob.htm
2. http://learning.mgccc.cc.ms.us/math/mathdocs/alg/howtomix.pdf (slightly different than what I did)
Solve the following word problems by setting up an equation and solving.
1. The sum of two consecutive integers is 315. Find the integers.
x   x  1  315
x  x  1  315
2 x  1  315
2 x  314
x  157
Answer :157,158
2. The sum of two consecutive even integers is 486. Find the integers.
x   x  2   486
x  x  2  486
2 x  2  486
2 x  484
x  242
Answer : 242, 244
3. The sum of three consecutive odd integers is – 3 . Find the integers.
x   x  2    x  4   3
x  x  2  x  4  3
3 x  6  3
3 x  9
x  3
Answer :  3, 1,1
4. Find two consecutive integers whose product is 5 less than the square of the smaller number.
x  x  1  x 2  5
x2  x  x2  5
x  5
Answer :  5, 4
(Day 17 Homework continued)
© Andrew McKintosh 2010
5. In order for Debbie to get an A in Biology she must have an average of 90 on four tests worth 100 pints each.
The scores on Debbie’s first three tests were 87, 92 and 84. What must Debbie get on the fourth test in order to earn
an A for the Biology course?
87  92  84  x
 90
4
263  x
 90
4
263  x  360
x  97
6. Hamish mixes Peanuts that cost $2.40 per pound with Cashews that cost $3.20 per pound to make an 80 pound
mixture that costs $2.96 per pound. How many pounds of each kind of nut did Hamish put into the mixture?
Peanuts
Cashews
+
=
2.40
3.20
80 – C
C
2.40  80  C   3.20C  2.96 80 
192  2.4C  3.2C  236.8
10 192  10  2.4C  10  3.2C  10  236.8
1920  24C  32C  2368
1920  8C  2368
8C  448
C  56
Answer: 56 pounds of Cashews and 24 pounds of Peanuts
7. What is 24% of 340?
x  .24  340
x  81.6
8. 48 is what percent of 960?
48  x  960 
48
x
960
.05  x
x  5%
1
% of what number?
5
1
12 
x
500
12  500   x
9. 12 is
6000  x
Mixture
2.96
80
Day 18 Homework: Topics: Solving quadratic equations
© Andrew McKintosh 2010
(factoring, square root property, completing the square with a = 1)
Supplemental Reading:
1. http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut17_quad.htm (stop after
example 7)
1. Solve the following quadratic equations by factoring and using the zero product rule.
A) 2x2  6 x  0
B) 49x2  36  0
C) x2  5x  6  0
D) x2  5x  6
2 x  x  3  0
7 x   6  0
 7 x  6  7 x  6   0
2
2x  0 x  3  0
x0 x3
2
 x  2  x  3  0
x2  5x  6  0
x 2  0 x 3  0
x2
x3
 x  3 x  2   0
7x  6  0 7x  6  0
6
6
x
x
7
7
3 2
x  8 x  20  0
F)
4
3
4  x 2  4  8 x  4  20  4  0
4
2
3 x  32 x  80  0
E) x2 10x  25  0
 x  5 x  5  0
x 5  0
x5
x3 0 x2  0
x  3 x  2
G) 14  9x2  15x
0  9 x 2  15 x  14
0   3 x  2  3 x  7 
3x  2  0 3x  7  0
 3x  20  x  4   0
2
x
3 x  20  0 x  4  0
3
20
x
x  4
3
2. Solve the following quadratic equations by “using the square root property”
A) 49x2  36  0
 x  5
B)
49 x  36
36
x2 
49
2
x
 28
x  5   28
2
x  5 47
x  5 2 7
36
6
x

49
7
C) 2  x  13  1  49
2
2  x  13  50
2
 x  13
2
 25
x  13   25
x  13  5
x  13  5
x  18, 8
3. Solve the following problems by completing the square
A) x  8x 15  0
x2  8x
2
 15
8
x  8 x  16  15  16
4
 x  4   31
16
 a  1
B) x  5x  6  0
x2  5x
2
2
5
2
x  4   31
x  4  31

5
2
25
4
 6
25 25
x2  5x 

6
4
4
2
5
25 24


x  
2
4
4

2
5
1

x  
2
4


5
1

2
4
5 1
x 
2 2
x
x  3, 2
7
3
Day 19 Homework: Topics: Solving quadratic equations
(completing the square  a  1 , quadratic formula)
© Andrew McKintosh 2010
Supplemental Reading:
1. http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut17_quad.htm (start with
example 8 BUT skip example 10)
1. Solve the following problems by completing the square
 a  1
A) 9x 18x  3  0
B) 9x2 12x 14  0
2
9 x 2  18 x
2
1
1
9 2 18
x  x
9
9
 3 

3
9
9 x 2  12 x
1
3
1
x2  2 x  1  1 
3
x2  2x
 x  1
x
2

4
3
4
14
x

3
9
4
4
14
4
x2  x   
3
9 9 9

2
3
2  18

x  
3
9



2
3
9 2 12
x  x
9
9
 14 

14
9
x2 
2
3
 x 1  
 x  1
6
3
3 6
3
4
9
2
x
2
 2
3
 x
2 3 2 23 2


3
3
3
2. Solve the following problems by using the Quadratic Formula.
(Did you notice that these next two problems are IDENTICAL to the two problems above? Did YOU get the same
answers as above?)
A) 9x2 18x  3  0
B) 9x2 12x 14  0
a  9 b  12 c  14
a  9 b  18 c  3
x
 18   4  9  3
2 9
18 
2
18  324  108

18
x
12 
 12 
2
 4  9  14 
2 9

12  144  504
18
x
18  324  108 18  216 18  36  6


18
18
18
x
12  144  504 12  648 12  324  2


18
18
18
x
18  6 6 6 3  6
3 6


18
18
3
x
12  18 2 6 2  3 6
23 6


18
18
3


C) 6  2x2  x
2x2  x  6  0
x
 1
1
 4  2  6 
2  2

D) x2 10x  25  0
a  1 b  10 c  25
a  2 b  1 c  6
2


x
1  1  48
4
1  47
 Not a Real Number.
4
(Note: later we will be able to say more about this)
x
x
10 
 10   4 1 25 10 

2 1
2
100  100
2
10  0 10  0 10


5
2
2
2
3. Use the Discriminant to determine the number of real solutions to each equation (do NOT solve!)
A) x2  8x  16
x 2  8 x  16  0
B) x2  7 x  12  0
b 2  4ac
b 2  4ac
 7 
 8 
49  48
1
two real solutions
2
 4 116 
64  64
0
one real solution
2
 4 112 
C)
x2  5x  12  0
b 2  4ac
 5
2
 4 112 
25  48
23
no real solutions
Day 20 Homework: Topics: Complex Numbers
© Andrew McKintosh 2010
Supplemental Reading:
1. http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut12_complexnum.htm
1. Write the complex number in standard for m ( a + bi )
A.
4  5
2i  5
5  2i
B. 5i  7i 2
5i  7  1
C. 4i  3  2i 2  7i3
4i  3  2  1  7i  i 2 
7  5i
4i  3  2  7i  1
5  3i
2. Add or subtract as indicated. Write your answer as a complex number in standard form.
 3 5   7 11 
A. 2  8  5  50
B.    i     i 
2 2  3 3 
3 5 7 11
2  2 2i  5  5 2i
  i  i
2 2 3 3
3  3 2i
9 15 14 22
  i  i
6 6
6
6
23 7
  i
6 6
3. Multiply. Write your answer as a complex number in standard form.

A.
 

B. 3i  5  2i 
3  2i 5  3i 
 2  3i  2  3i 
15i  6i 2
15  9i  10i  6i 2
4  6i  6i  9i 2
90i 2
15i  6  1
 3  2i 
 3  2i  3  2i 
15  i  6  1
4  9  1
9  6i  6i  4i 2
9 10  1
6  15i
15  i  6
49
9  12i  4  1
21  i
13
9  12i  4
15  6
15i  6i
3 10
C.
D.
E.
2
5  12i
4. Write the quotient as a complex number in standard form.
A. 2  2  i  2i  2i  2 i
5i 5i i 5i 2 5  1 5
B.
5
5 2  3i 10  15i 10  15i 10  15i 10  15i
10 15






  i
2  3i 2  3i 2  3i
4  9  1
49
13
13 13
4  9i 2
C.
2  3i 2  3i 3  5i 6  10i  9i  15i 2 6  10i  9i  15  1 6  10i  9i  15 21  i 21 1







 i
3  5i 3  5i 3  5i
9  25  1
9  25
34
34 34
9  25i 2
5. Solve the following Quadratic equations. Write your answers as complex numbers in standard form.
3 2
x  6x  9  0
A. 4x2  2x  3  0
B.
2
2
*2  3x 2  12 x  18  0
2   2   4  4  3
x
x2  4 x  6  0
 3
2  4
2  4  48
8
2  44

8


2  4 11 1
8
2  2 11i 2 2 11
1
11

 
i 
i
8
8
8
4
4
x
4
 4 
2
 4 1 6 
2 1
4  16  24
2
4  8 4  2 2i 4 2 2


 
i  2  2i
2
2
2
2

Day 21 Homework: Topics: Polynomial Eqns. (Eqns. that “look” quadratic),
© Andrew McKintosh 2010
Single radical Eqns.
Supplemental Reading:
1. http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut18_polyeq.htm
2. http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut20_quadform.htm
3. http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut19_radeq.htm (ex 1 & 2)
1. Solve the following equations.
A. x4  81  0
B. x6  7 x3  8  0
 x   9  0
 x  9  x  9   0
 x  9    x    3   0
 x  9   x  3 x  3  0
2 2
2
2
2
2
2
x
x3 0
x3  0
x  9
x  3i
x  3
x3
3
x  2
x  1  0 x 2  1
x 1
x  i

 x
2
2
 4 1 4 
1
2
2
1
1
2
x3 

x  10  16
x  26
  4
x
1 
1
G.
3

3
2 x  5  3
2x  5

3
  3 
1
x3 1  0
1
3
 13 
3
 x   1
 
3
x 1
H. x  31  9 x  5
31  9 x  5  x
3
2 x  5  27

2 x  32
x  16
31  9 x  25  5 x  5 x  x 2
31  9 x

2
 5  x 
 4 11
2 1
x3  1
3
2
1  1  4
2
1  3
x
2
1  3i
x
2
1
3
x 
i
2 2
5
2
 13   5 
x   
   2 
125
x
8
2
x2  x  1  0
x
2x3  5  0
x  10  4  0
2
x 1
2 1
1
1
 
2
x  10
 2 
2
No Solution
x  10  4

x
x 1  0
x  5
1
x
4
F.
x2  2x  4  0
 13
 1 
 2 x  5   x 3  1  0



1
2
x
0
2 x 3  3x 3  5  0
x 5  0
2 x 1
3
E. 3x 3  2 x 3  5  0
x 5  0
2 x 1  0
 1
x  1  3i
D. 2 x  9 x  5  0

3
2  4  16
2
2  12
x
2
2  2 3i
x
2
 x  1  x 2  1  0
x 1
  x 
x
2
x 2  x  1  1 x  1  0
2
3
x20
C. x  x  x 1  0
3
  2
 x  2   x 2  2 x  4   x  1  x 2  x  1  0
2
2
 8  x 3  1  0
 x 
2
x2  9  0
3
2
0  x2  x  6
0   x  3 x  2 
x  3 x  2
Day 22 Homework: Topics: Equations w/ 2 radicals, rational exponents,
© Andrew McKintosh 2010
rational equations, absolute value eqns.
Supplemental Reading
1. http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut19_radeq.htm (ex 3 & 4)
2. http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut15_rateq.htm
3. http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut21_abseq.htm
1. Solve the following equations.
x  x 5 1
x  1 x  5
B. 2 x  1  2 x  3  1
A.
 x   1 
2
x5
2 x 1  1 2x  3

2
2
x 1
  1 
2
2x  3

2
x  1 x  5  x  5  x  5
4  x  1  1  2 x  3  2 x  3  2 x  3
x  x 4 2 x 5
4x  4  2x  4  2 2x  3
4  2 x5
2x  2 2x  3
2  x5
 2
2


x  2x  3
x5

2
 x
4  x5
9x
2


2x  3

2
x2  2x  3
x2  2x  3  0
 x  3 x  1  0
x  3 x  1
note : x  1 is extraneous so only x  3
2
C.
 x  23
9
3
2 4m  4
  2
m2 m m 4
3
2
4m  4
 
 m  2  m  m  2  m  2 
D.
3
2 2
3


  x  23   9 2


m  m  2  m  2  
x  2  2 93
x  2  999
x  2  333
x  2  27
x  25
 4m  4 
3
2
 m  m  2  m  2    m  m  2  m  2  
m
 m  2
 m  2  m  2 
3m  m  2   2  m  2  m  2   m  4m  4 
3m 2  6m  2m 2  8  4m 2  4m
m 2  2m  8  0
 m  4  m  2   0
m  4 m  2
note : m  2 is extraneous so only m  4
E. 2 2x  1  1  9
F. x 2  6 x  18  3 x
2 2 x  1  10
x 2  6 x  3 x  18
2x 1  5
x 2  6 x  3x  18
2 x  1  5 2 x  1  5
2x  6
2 x  4
x3
x  2
x 2  3x  18  0
x 2  6 x    3x  18 
x 2  9 x  18  0
 x  6  x  3  0
 x  6  x  3  0
x  6
x  6
x3
x  3
x  6,3, 3  all work ! Did you check ? 
2. Find an equation that has 1, 1, i,  i as it’s solutions.
 x  1 x  1 x  i  x  i   0



2
1 x 2  1  0Topics: Solving Linear and Absolute Value Inequalities
Day x23Homework:
Supplemental
x 4  1  0 Reading:
© Andrew McKintosh 2010
1. http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut22_linineq.htm
1. Solve the following inequalities. Give your answer in all three forms that we did in class (inequality, graph and
interval notation).
A. 3x  15
B. 2 x  5  17
2 x  12
x  6
x5
 , 5
 , 6 
5
-6
1
2
 x  3  4 x  1  12  x    7
2
3

1
3
 x   4 x  1  12 x  8  7
2
2
1
3
  2  x   2    2  4 x  1 2    2 12 x   2  8  7  2 
2
2
 x  3  8 x  2  24 x  16  14
7 x  1  24 x  2
17 x  1  2
17 x  1
1
x
17
1


  17 ,  


C. 
- 1/17
D. 1  2 x  3  9
2  2 x  6
1  x  3
E. 3.4 x  1.7  5.1
10  3.4 x  1.7 10   5.110 
34 x  17  51
34 x  68
x2
 1, 3
- 1
 2,  
3
2
F. 2 3x  7  4  12
G. 9  2 x  2  3
2 3x  7  8
9  2 x  1
3x  7  4
This inequality has NO SOLUTION
because an absolute value can NEVER
be less than a negative number!
3 x  7  4 3 x  7  4
3 x  11
3x  3
x
11
3
x 1
1
11/3
 ,1  
11 
,
3 
11
x  1 or x 
3
Day 24 Homework: Topics:
Supplemental Reading:
Solving Polynomial Inequalities
© Andrew McKintosh 2010
1. http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut23_quadineq.htm
2. http://www.youtube.com/watch?v=pV3cZ1zbuvs
3. http://www.sosmath.com/algebra/inequalities/ineq05/ineq05.html
1. Solve the following Polynomial inequalities. Give your answer in all three forms that we did in class (inequality,
graph and interval notation).
A. x2  4x  4  9
x2  4x  5  0
B. x2  6   x
x2  x  6  0
 x  5 x  1  0
-5
 x  3 x  2   0
1
x  5 or
-3
3  x  2
x 1
 3, 2
 , 5   1,  
C. x3  3x2  9x  27  0
x 2  x  3  9  x  3  0
D. x3  3x2  x  3  0
x 2  x  3   1 x  3   0
 x  3  x2  1  0
 x  3 x  1 x  1  0
 x  3  x 2  9   0
 x  3 x  3 x  3  0
2
 x  3  x  3  0
-3
x  3 or
3
-3
x3
 2 x  13  x 2  4   0
 2 x  13 x  2  x  2   0
2
 4 1 5 
2 1
8  64  20
2
8  84
x
2
8  4  21
x
2
8  2 21
x
2
-13/2
x
x
x 1
F. 2x3  13x2  8x  52  0
x 2  2 x  13  4  2 x  13   0
x2  8x  5  0
x
1
 3, 1  1,  
E. x2  8x  5
x2  8x  5  0
8
-1
3  x  1 or
 , 3  3,3
8 
2

2 4  21
2
x  4  21

-2
2
13
 x  2 or x  2
2
 13

  2 , 2    2,  



4  21
 4  21
4  21  x  4  21
 4  21, 4  21 


Day 25 Homework: Topics: Solving Rational Inequalities
Supplemental Reading:
© Andrew McKintosh 2010
1. http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut23b_ratineq.htm
1. Solve the following Rational inequalities. Give your answer in all three forms that we did in class (inequality,
graph and interval notation).
x  12
3 0
x2
 x  2
x  12
3
0
x2
x2
x  12  3 x  6
0
x2
2 x  6
0
x2
4
1

x  5 2x  3
4
1

0
x  5 2x  3
4  2 x  3
1 x  5 

0
 x  5 2 x  3  2 x  3 x  5 
A.
B.
8 x  12  x  5
0
 x  5 2 x  3
7x  7
 x  5 2 x  3
-2
0
3
-5
-3/2
-1
2  x  3
 2,3
C.
3
 x  1
2
3
 , 5    , 1
 2

x  5 or
1
1

x x3
D.

5
2x

1
x 1 x 1
1
1

0
x x3
1 x  3 
1x

0
x  x  3 x  x  3
5
2x

1  0
x 1 x 1
5  x  1
2 x  x  1
1 x  1 x  1


0
 x  1 x  1  x  1 x  1  x  1 x  1
x 3 x
0
x  x  3
5x  5  2 x2  2 x  x2  1
0
 x  1 x  1
3
0
x  x  3
3 x 2  7 x  6
0
 x  1 x  1
  3x 2  7 x  6 
-3
x  3 or
0
x0
0
 x  1 x  1
  3 x  2  x  3
0
 x  1 x  1
 , 3   o,  
-1
-2/3
1
3
2
 x  1 or x  3
3
2
 , 1   ,1  3,  
 3 
Day 26 Homework: Topics: Slope, Y-intercept, Slope-Intercept form,
© Andrew McKintosh 2010
Parallel lines, Perpendicular Lines
x  1 or

Supplemental Reading:
1. http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut25_slope.htm
2. http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut26_eqline.htm
3. http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut27_graphline.htm
4. http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut28_parpen.htm
1. Find the slope and the y-intercept for the following lines.
2
A. y   x  5
B. 2x  3 y  6
C. y  1
D. x  3  4
3
2
2
m0
x 1
2
y  x2 m 
m
3
3
3
y  int   0, 1
m  undefined
y  int   0, 2 
y  int   0,5 
y  int  none
2. Find the slope-intercept form of the equation of the line with the given characteristics.
1
A. Passes through the point  3, 4  and slope = 
3
1
y   xb
3
1
4    3   b  4  1  b  3  b
3
1
y   x3
3
B. Passes through the point  5, 2 and slope = 0
Slope = 0 so horizontal line!
D. Passes through the two points
m
Y=2
C. Passes through the point  5, 2 and slope = undefined
Slope = undefined so vertical line!
X=5
 2,5 and 3,7 
y2  y1
75 2


x2  x1 3  2 5
2
2
35 6
29
x  b  7   3  b 
 b 
b
5
5
5 5
5
2
29
y  x
5
5
3. Find the slope-intercept form of the equation of the line with the given characteristics THEN sketch the line!
y
A. Passes through the point  1, 4  and is parallel to the line 2 x  y  4
2x  y  4  2x  4  y
So the slope of THAT line is m = 2.
Since MY line is parallel to that line then my line
must also have slope m = 2.
y  2 x  b  4  2  1  b  6  b
y  2x  6
B. Passes through the point  2,3 and is perpendicular to the line 2x  3 y  4
2x  3y  4 
2
4
y   x
3
3
So the slope of THAT line is m   2 .
3
3
Since my line is perpendicular to that line my m  2
3
3
y  x  b  3   2  b  0  b
2
2
3
y  27x Homework: Topics: Relations, Functions, Domain, Range,
Day
2
Function notation, Piecewise-defined functions
© Andrew McKintosh 2010
Supplemental Reading:
1. http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut30_function.htm
1. Determine if the following relations represent functions or not. Also list the Domain and Range for each relation.
A.
 1, 2  ;  2,5 ;  3, 2  ; 5, 1
B.
 1, 2  ;  2,5 ;  3, 2  ;  2, 1
Yes it is a function
No it is NOT a function
D : 1, 2,3,5
D : 1, 2,3
R : 2,5, 1
R : 2,5, 1
C.
4
6
3
0
D.
4
6
3
0
2
Yes it is a function
2
No it is NOT a function
D : 4,3, 2
D : 4,3, 2
4
R : 6, 0, 4
R : 6, 0
2. Evaluate the following functions as indicated.
A. f  x   2x  3x2
Find
f  0
f  2
f  2
f 1
f  0  2  0  3 0  2  0  3 0  0  0  0
2
f  2   2  2   3  2   2  2   3  4   4  12  16
2
f  2   2  2   3  2   2  2   3  4   4  12  8
2
f 1  2 1  3 1  2 1  3 1  2  3  1
2
 x2  2

B. g  x   4
2 x  5

if x  2
if  2  x  2
Find
f  3
f  3
f  0
f  2
f  2
if x  2
f  3  2  3  5  6  5  1
f  3   3  2  9  2  7
2
f  0  4
f  2    2   2  4  2  2
2
f  2  4
3. f  x   x2  2x  1
g  x   3x  3 . Find all values of x such that f  x   g  x 
x 2  2 x  1  3x  3
x2  x  2  0
 x  2  x  1  0
x  2 x  1
Day 28 Homework: Topics: Finding Domain and Range,
© Andrew McKintosh 2010
Function values from a graph, increasing, decreasing,
Finding x-intercepts algebraically, odd and even functions.
Supplemental Reading:
1. http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut31_graphfun1.htm
2. http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut32_graphfun2.htm
1. Given the following graph of y  f  x  , find the following…..
A. The Domain of y  f  x 
B. The Range of y  f  x 
 ,3
 3,  
C. What is the y-intercept?
 0, 1
D. How many x-intercepts does this graph have?
Three
E. Is this graph a function? (Explain why or why not)
Yes this is the graph of a function. We can tell because the graph passes the vertical line test.
F. What is f 1
f 1  3
f  1
f 3
f  1  1
f 3  4
G. List all value of x for which f  x   2
x  3 x  2
H. List the intervals on which the graph is increasing and decreasing.
The function is increasing on  2, 1 and 1,3 and is decreasing on  , 2 and
 1,1
2. Without graphing, find the x-intercepts for f  x   4x3  24x2  x  6
0  4 x 3  24 x 2  x  6
So the x-intercepts for the function are….
1
1
 6,0   ,0   ,0 
 2  2 
0  4 x 2  x  6   1 x  6 
0   x  6   4 x 2  1
0   x  6  2 x  1 2 x  1
x6
x
1
2
x
1
2
3. Given the two functions, g  x   3x4  5x2  7
and
h  x   2x3  4x , determine whether they are even
functions, odd functions of neither.
g  x  3 x  5  x   7
4
2
 3x  5 x  7
4
2
 g  x
So, g  x  is an even function
h   x   2   x   4   x   2 x 3  4 x    2 x 3  4 x    h  x 
3
So, h  x  is an odd function