College Algebra Final Exam

[Answers at end.]

 

1)  Find the solution set for:

y(y + 8)(y - 8)(2y – 5) = 0

a)   y = 8, y = -8, y = 5

b)   y = 0, y = 8, y = -8, y = 5

c)   y = 0, y = -8, y = 8, y = 2.5

d)   y = 0, y = -8, y = 8, y = -2.5

e)   none of these
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2)  Solve the equation:  
a)
b)

c)  
d)  

e) none of these

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3)  Solve for t:    

a)  

b)     

c)  

d)   

e) none of these

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4) The equation of a circle with radius 7 and center (1,-3) is:

a)

b)

c)

d)

e)    none of these

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5) Consider the circle with center (-3,1) and radius of 5.

Determine which of the following points is on the circle.

 

a) (-9,-4)          b) (1,4)                        c) (1,-7)           d) (15,0)          e) none of these

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6)  Which of the following describes the transformation of the basic function,, if ?

a) b(x) is shifted right 3 units

b) b(x) is shifted up 3 units

c) b(x) is shifted left 3 units

d) b(x) is shifted down 3 units

e) none of these

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7) Which of the following is the correct Domain and Range for ?

a) Domain is; Range is.

b) Domain is; Range is.

c) Domain is ; Range is 

d) Domain is  Range is

e) None of these

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8) If a function f(x) has the ordered pair (3,5) on its graph, then f – 1(x) will have which point on its graph: 

a) (0,0)           b) (-3,-5)               c) (-3,5)                      d) (5,3)              e) none of these

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9) Which is the equation of a line parallel to 4x – y = 6 and passes through the point (1,5)?

a) y = 4x + 5

b) y = 4x + 1

c) y = -1/4 x + 1

d) y = -1/4 x + 5e) none of these

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10) Find a linear function such that f(0) = 11 and f(1)= -5

a) f(x) = 6x  - 11

b) f(x) = 16x + 11

c) f(x) = -6x - 7

d)  f(x) = -16x +11

e) none of these

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11)  Find the vertex of

a) (5, 57)

b) (-5, -57)

c) (5, 157)

d) (-5, -93)

e) none of these

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12) Solve the system of equations:         

 

a) (-21,54)         b) (21,-54)         c) (21,54)          d) ( -21,-54)      e) none of these

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13) If a system consists of an equation of a line and an equation of a circle, what is the largest number of possible solutions?

a) 4      b) 3      c) 2      d) 1      e) none of these

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14) If the power function of a polynomial function is , then the end behavior will be:

            a)                             c)

b)                               d)

e)  none of these

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15) Odd functions have symmetry about

a) origin        b) the x-axis           c) the y-axis                      d) the y = x line                  e) none of these

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16) Given the function  what will be the maximum number of turning points possible

for the graph of f(x).

a) 1                  b) 2                  c) 3                  d) 4                  e) none of these

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17) Given the function , find the y-intercept(s).

 

 (a) 2340                      (b) 0                 (c) -12,13,15   (d) -2340         (e) none of these

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18) A rough sketch for  the graph of is:

a)                                 b)                                             c)            d)                   

 

 

e) None of these

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19) Simplify and solve using properties of logs:        .

(a)      (b)                       (c)                      (d)         (e) none of these

 

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20) Solve for x:           
a)   

b) x = 7
c)  undefined
d)

e) none of these

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21) Solve the equation:

a)

b) 

c)
d)

e)  none of these

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22) How long will it take an investment of $20,000 to double if it is compounded continuously at a rate of 5%

(Answer is rounded to the nearest tenth)?

a) 3.7 years            b) 1.4 years                  c) 0.1 year        d) 13.9 years   

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23) The half-life of a radioactive substance is 42 days.  Find the decay constant, k, for the equation:

a) -0.000165                b) -0.0165       c) -29               d) 29                           

24) Solve for x:

a) x = 4 and -1             b) x = 4 only      c) x = -1 only             d) x = 3 and 0              e) none of these

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25) Given , find the composition .

a)        b)           c)        d)    e) none of these

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26) Given , which pair of functions can create a composition equal to h(x)?

a)                          b)

c)                          d)              

27) Which composition for problem # 26 is going to create h(x), assuming you use the functions you chose?

a) f(g(x))          b) f(f(x))          c) g(f(x))          d) g(g(x))         e) none of these

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28-29:Given the function , determine its range by first finding its inverse.

28) The inverse for f(x) is:

a)               b)            c)

d)               e) none of these

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29) The range for the original function: is:

a)              b)              c)

d)              e) none of these

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y

 

30) A rectangular yard is to be constructed along the side of a house using a fence on three sides, as shown.  The house wall will serve as the fourth side. Find the dimensions that produce the maximum area if 40 meters of fence is available.

 

 

 

 


 

 

house

 

x

 

x

 

a) 10 x 10

 

b) 10 x 20

c) 10 x 30

d) 10 x 38

e) none of these

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31) Determine if the function is even, odd, both or neither.

a) even             b) odd               c) both              d) neither

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32) Given the graph shown, give the polynomial it represents

a)

b)

c)

d)

e) none of these

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33-34 Choose the graph for the polynomial function by first factoring the function to find its zeroes.

33) If , the zeroes will be:

a) 8,-48 and 72              b) -6,3,0            c) 0,9,-3            d) 0,3    e) none of these

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34) the graph for this polynomial function will be :

 

 

 

 


 

a)                                                                                 b)

 

 

 

 

 

 

 
 

c)                                                                                 d)

 

 

 

 

e) none of these

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35) Given the rational function , what will be a vertical asymptote?

a) x = -1/2         b) y= -1/2          c) x = 2             d) y = 2             e) none of these

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36) Given the rational function , what is its y-intercept?

a) (0,4)             b) (0,-2)            c) (0,2)             d) (0,0)

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37) Given the rational function , what is the equation for its horizontal asymptote(s)?

 

a) y = 3             b) y = -1/3         c) x = ±2           d) x = 4             e) none of these

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38) Given the function , the x-intercepts are:

 

a)         b)                   c)          d)                    e) none of these

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39) Carl bought a new computer on sale for $1500.  If the sale price was 15% off the original price, what was the original price?

a) $1275           b) $1725           c) $1764.70       d) $1304.35       e) none of these

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40) Find the x-intercept for the function .

a) (8,0)             b) (5,0)             c) (2,0)             d) (3.32,0)         e) none of these

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41) If $5000 is invested in a bank that offers 3%, compounded quarterly, how much will be in the account after 3 years?

a) $5470.87       b) $450.00         c) $5450.00       d) $5469.03       e) none of these

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42) What is the range for the function ?

a) (-∞,-3]          b) (0,∞)                        c) (-3,∞)           d) (-∞,3)           e) none of these

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43) Given the graph of a rational function           

A possible denominator is:

a) (x2+1)(x2-1)

b) x2(x+2)

c) (x2-1)(x+1)

d) x(x+2)

e) more than one of these

 

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ANSWERS

#1        c

#11      e

#21        b

#31       d

#2       b

#12      c

#22        d

#32       a

#3       a

#13       c

#23        b

#33       d

#4       d

#14       b

#24        b

#34        b 

#5       b

#15       a

#25        d

#35        c  

#6      c

#16        c

#26       c

#36        d

#7      d

#17       a

#27        c

#37        a

#8      d

#18       c

#28         b

#38        a

#9      b

#19       b

#29        c

#39        c

#10    d

#20        a

#30        b

#40        b

 

#41    d             #42     c                        #43     e

 

You will be graded on 40 questions, and this Spring there will be 42 multiple choice and four open questions to be shown on the actual final that will not have multiple choice.