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FST
Chapter 1 Review
1.
Name _______________________________
9/10/13
Based on the discriminant, determine the number of real solutions of the quadratic and
solve. Factoring, Completing the Square, Square Root Property or Quadratic Formula
(you will have to use each method at least once).
a.
x 2 " 6x +13 = 0
b 2 " 4ac
b.
b 2 " 4ac
# of real solutions
! Solution method/solve:
!
# of real solutions
! Solution method/solve:
!
c.
2
2( x " 2) +1 = 11
b 2 " 4ac
d.
!
x 2 + 2x = 15
b 2 " 4ac
# of real solutions
# of real solutions
! Solution method/solve:
! Solution method/solve:
!
e.
2x 2 +12x + 7 = 0
b 2 " 4ac
f.
4 x 2 " 20x + 25 = 0
b 2 " 4ac
# of real solutions
! Solution method/solve:
!
2x 2 " 24 x + 40 = 0
# of real solutions
! Solution method/solve:
!
2.
a.
Solve by factoring.
x 3 " 7x 2 " 3x + 21 = 0
!
x 4 "1 = 0
b.
4
7
=
2x " 3 3x " 5
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3.
Solve by finding a common denominator.
a.
3x
7
1
" 2
=
x + 3 x + 3x x
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4.
a.
Solve by squaring both sides. Remember radicals should be on OPPOSITE sides of =.
b.
3x + 4 = 2 " x + 2
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x + 7 " x =1
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5.
Solve. Hint: Remember to take the reciprocal power.
a.
2( x + 2) 3 = 18
2
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b.
3
b.
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3( x +1) 4 " 9 = 15
6. Graph you solutions AND state the solution in Interval Notation.
a. -5x – 3 ≤ 7
b. 16 ≤ 6x-2 ≤ 40
7. Graph your solutions AND state the solution in Set Notation.
a. 5x – 8 > 7 or 8x – 5 ≤ -25
b.
-9 ≤ -4x+3 ≤ 12
8. Solve each of the following absolute value problems. Show work and circle your answer.
a. |5x – 3| = 7
b. |6x – 4| < 20
c.
d. 6 -3|2x + 1| ≥ -36
8|4x-2|- 3 ≥ 61
9. Simplify, stating your answer in complex form.
a. (4 + 6i)(8 – 2i)
b.
!
d. i326 + i250
7 + 3i
2 + 3i
c. (4 + 8i)2
FST
Chapter 2 Review
Name_________________________
Determine (a) the domain of the relation, (b) the range of the relation, (c) if the relation is a
function, and (d) the equation of the function.
1.
2.
a. D:
a. D:
b. R:
b. R:
c.
c.
d. equation:_________________________
d. equation:________NONE!!!__________
3.
4.
a. D:
a. D:
b. R:
b. R:
c.
c.
d. equation:__________________________
d. equation:_____NONE!!!_____________
5. Given the functions f(x), g(x), and h(x), evaluate:
f (x) = ( x +1)
2
a. f ! h ( x )
!
g(x) = 2x +1
h(x) = 3x
b. g( h ( x ))
c. g ! g( x )
!
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!
6. Given 5x " 6y = 30 ,
a. Write an equation that is parallel and goes through the point (–2, 8).
!
b. Write an equation that is perpendicular to 5x " 6y = 30 and goes through the
point (–2, 8).
!
7. Find the difference quotient for f (x) = x 2 + "3x +11.
!
8. Graph each function.
a.
f (x) = "2( x +1)
2
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c.
3
3
d. p(x) = 3 x + 2
h(x) = ( x " 4 ) +1
!
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e.
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b. g(x) = x " 5 " 3
m(x) = 0.5 x + 5
f. n(x) = " x + 6
!
9. State the equation and graph the circle that has its center at (5, -7) and travels through (0,5).
Scale the graph as needed to show the entire circle.
Equation:
10. State the center, radius, and 4 points that the circle of (x " 6) 2 + (y " 3) 2 = 64 would travel
through.
Center: ____________
Radius: _______________ Points:
!
11. Decide if each graph is even, odd, or neither and give justification for your decision.
Decision:
Decision:
Justification:
Justification:
12. Algebraically determine if the function is even, odd, or neither.
1
a.
f (x) = 3x 3 " 2x
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b.
b(x) = x 5 " 3
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13. If f (x) = 3x " 4 & g(x) = "2x + 6 , state each equation and its domain. Then find the
requested value.
a. (f+g)(x)
b. (f•g)(x)
c.
(f/g)(x)
!
d. (f+g)(5)
14. If f (x) = 5 & g(x) = 3x "1 , state each equation and its domain. Then find the requested
value.
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a. (f-g)(x)
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b. (f/g)(x)
c.
(f/g)(6)
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b(x) = (x "1)(x + 4)(x " 5) !
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c(x) = (x +1) 2 (x " 3)(x + 2) 2 !
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FST
Chapter 4 Review
Name___________________________
2. Graph f (x) = 2( 3)
1. Graph f (x) = log 2 ( x "1) " 3
10
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-10
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8
6
6
4
4
2
2
5
10
-10
-5
5
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
Given f ( x ) = 2x 3 + 5 and g( x ) = 2x 2 " x ,
3.
a. Is f(x) a one-to-one function?
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+4
10
8
-5
x +2
!
b. Is g(x) a one-to-one function?
c. Algebraically determine the inverse of g(x).
d. Algebraically determine if f(x) and g(x) are inverses of each other.
10
4.
Sketch the inverse of each function. Is the inverse a function? Explain.
5.
Solve by rewriting each expression with a common base raised to a power.
a. 16
x +1
1x
b.
= 27 2
3
= 32
!
c. 25 x +1 = 625 x
!
!
6. Evaluate:
" 1 %
a. log 5 $
'=
#125 &
lne 5 =
e.
log 7 1 =
f.
! 1$
! 49 $
log 7 # & ' log 7 # & =
" 5%
" 5%
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b.
log 4 ( 32) =
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c.
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d.
log 4 32 + log 4 2 =
7. Condense each expression.
a. 3log 8 4 ! log 8 16
b. log 3 625 ! log 3 125 + 3log 3 2
8. Expand each expression.
" x2y %
a. log 7 $ 3 '
# z &
b. log( abc )
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9.
Evaluate. No work necessary.
a. log 4 64
!
4
c. log121 11
b. log 3
!
1
27
d. log 5 5 7
!
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e. log 1000
f. ln1
!
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10. Your grandparents open a savings account for you and invest $7500 in an account that pays
3.25% interest monthly. When will the balance in your account double?
!
11. You invest $5,400 at 3.25% interest that is compounded continuously. Calculate the value of
your investment in 12 years.
12. You invest $2,300 in an account with an interest rate of 4.5% compounded continuously.
How long will it take your investment to triple?
11. Solve.
a. log 2 x + log 2 (x ! 2) = 3
b. 2ln x + 3ln2 = 56
!
c. log 3 x + log 3 5 = log 3 30
d. log 8 10 ! log 8 ( 7 ! x ) = log 8 x
e. 3ln( x "1) = 150
f. 2" 4 x = 32
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h. 4e x " 5 = 31
g. 9 x ! 12 3x = !27
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!FST
Graph two cycles of each function.
1. y = 4 " 2sin(0.5x )
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2.
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Name_____________________________
4. y = "4 " 2csc( x + # )
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5.
y = "1+ 3tan x
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1
y = 1+ 0.5sin x
2
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