MA112 Precalculus Algebra
Fall 2010
Practice Final
1. Find the equation of the line
a. that passes through the points (-2, 1) and (1, -4).
b. with slope 3 that passes through (1,0).
2
c. parallel to y  5 x  2 that passes through (-1,-1).
2. Find the domain and the range of the following functions:
a.
b.
c.
d.
1
x4
f ( x)  4 x 3  x
f ( x) 
f ( x)  6  2 x
1
f ( x)  2
x
 3x  1, if x  1
3. Given f ( x)   2
 x  1, if x  1
a. find f (1) , f (0) , f (1) , f (2)
b. sketch an accurate graph of f .
4. Given f ( x)  3x  2
a. sketch an accurate graph of f ,
labeling the x- and y-intercepts
b. state the domain of f (x)
c. state the range of f (x)
5. Find the composition  f  g x
a. for f ( x)  2 x  1 and g ( x)  3x  1
1
1
b. for f ( x )  and g ( x) 
x
2x
3
c. for f ( x)  x and g ( x)  2 x 2
6. Compute the following and simplify in form a  bi :
a. 5  7i   2  4i 
b. 3i  2  i 
c. 2  3i   2  3i 
3  2i
d.
1  4i
7. Find the vertex of the parabola y  x 2  4 x  7 .
8. Quadratic Equations
a. Given the function f ( x)  6 x 2  24 x  30 :
express it in the standard form f ( x)  a x  h   k
 express it in the factored form f ( x)  ax  x1 x  x2 
b. Sketch an accurate graph of f ( x)  2 x 2  2 x  12 given that in standard form
2

2
1  25

f ( x)  2 x   
and in factored form f ( x)  2x  2x  3 . Label the vertex and
2
2

the x- and y- intercepts.
9. Match the equation with the graph.
a. y  xx  2 x  2
2
b. y  xx  2x  2
2
c. y  xx  2x  2
d. y  x 2 x  2x  2
10. Find the specified polynomial. You may leave your answer in factored form.
a. Provide the equation of a polynomial of degree 3 having root x  3 of multiplicity 1, root
x  0 of multiplicity 2 that goes through the point (1,-4).
b. Provide the equation of a polynomial of degree 3 having root x  3 of multiplicity 1, root
x  1 of multiplicity 2 that has y-intercept (0, 15).
11. Find the vertical and horizontal asymptote(s), if any, for the graph of the following functions:
a.
b.
c.
d.
1
6 x
1
f ( x)  2
x 9
1  3x
f ( x) 
x2
x3  x
f ( x) 
x
f ( x) 
3x 2  5 x  2
6x 2  2
find the y-intercept
find the x-intercept(s)
find the horizontal asymptotes, if any
find the vertical asymptotes, if any
12. Given f ( x) 
a.
b.
c.
d.
13. Find the inverse function f
1
a. f ( x) 
6 x
b. f ( x)  x 5  1
1
( x) for the following functions:
2
x2
3
a. find f 1 (the inverse function of f )
14. Given f ( x) 
b. sketch an accurate graph of
f and f 1
15. Match the equation with the graph.
a. y  e x 1  2
b. y  e x  1
c. y  2e x
d. y  e  x
16. Find the following:
 1 
a. log 4  
 64 
b. log 3 27 
c.
5 log5 6
17. Use the properties of logarithms to solve the given equations:
a. log 3 2  x   2
1
b. log x 3 
3
c. 2 ln x  ln( 4 x  6)  ln 2
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18. A bacteria culture doubles in size every 3 hours.
a. If the bacteria population is initially 2000 bacteria, find an expression for the number of
bacteria after t hours.
b. Find the number of bacteria that will be present after 5 hours.
c. When will the bacteria population reach 6500 bacteria?