Math 171 Spring 2008
Final Exam
Name___________________________________
May, 2008
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
By graphing the function, visually estimate its domain and range.
1) g(x) =
8-x
A) Domain = (-∞, 8] ; range = (-∞, 8]
B) Domain = [8, ∞) ; range = [8, ∞)
C) Domain = (-∞, ∞) ; range = (-∞, ∞)
D) Domain = (-∞, 8] ; range = [0, ∞)
Determine the equation of the line described. Put answer in the slope-intercept form, if possible.
2) Through (-8, 9), perpendicular to -2x - 7y = 79
7
8
79
A) y = - x + 37
B) y = x +
2
7
7
C) y =
7
x + 37
2
D) y =
2
2
x+
7
7
Determine whether the equation represents y as a function of x.
x-6
3) Given that y =
.
x+5
A) Yes
B) No
Find an equation for the circle.
4) Endpoints of a diameter (-6, 10), (0, 0)
A) (x + 3)2 + (y - 5)2 = 34
B) x2 + (y - 5)2 = 9
C) (x + 3)2 + y2 = 25
D) (x - 5)2 + (y + 3)2 = 34
Find an equation of the inverse relation.
5) x3y = 3
A) y3 = 3
B) y3 x = 3
C)
x3
=3
y
D) x3 =
Find the requested function value.
6) Find (g ∘ f)(3) when f(x) = -3x + 3 and g(x) = 4x2 + 4x - 4.
A) 116
B) -52
C) -57
1
D) -129
y
3
Given the polynomial function f(x), find the rational zeros, then the other zeros (that is, solve the equation f(x) = 0), and
factor f(x) into linear factors.
7) f(x) = x3 - 8x2 + 17x - 30
A) 6, -1 + 2i, -1 - 2i; f(x) = (x - 6)(x + 1 - 2i)(x + 1 + 2i)
B) -6, 1 + 2i, 1 - 2i; f(x) = (x + 6)(x - 1 - 2i)(x - 1 + 2i)
C) 6, 1 +
5, 1 -
5 ; f(x) = (x - 6)(x - 1 -
5)(x - 1 + 5)
D) 6, 1 + 2i, 1 - 2i; f(x) = (x - 6)(x - 1 - 2i)(x - 1 + 2i)
Graph the function, showing all asymptotes (those that do not correspond to an axis) as dashed lines. List the x- and
y-intercepts.
x2 - x - 12
8) f(x) =
x+4
A) x-intercepts: (-3, 0) and (4, 0) ,
y-intercept: 0, - 3
B) x-intercepts: (-3, 0) and (4, 0) ,
y-intercept: 0, 3
20
20
10
10
-20
-10
10
20
-20
-10
10
-10
-10
-20
-20
2
20
C) x-intercepts: (-3, 0) and (4, 0) ,
y-intercept: (0, -12) ;
-20
D) x-intercepts: (-3, 0) and (4, 0) ,
y-intercept: (0, 12) ;
20
20
10
10
-10
10
20
-20
-10
10
-10
-10
-20
-20
20
Graph the function.
9)
4, for x ≥ 1
f(x) =
-3 - x, for x < 1
6
y
4
2
-6
-4
-2
2
6 x
4
-2
-4
-6
A)
B)
6
-6
-4
y
6
4
4
2
2
-2
2
4
6 x
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
3
y
4
6 x
C)
D)
6
-6
-4
y
6
4
4
2
2
-2
2
6 x
4
-6
-4
-2
y
2
-2
-2
-4
-4
-6
-6
4
6 x
Graph the plane curve given by the parametric equations. Then find the equivalent rectangular equation.
10) x =
t, y = 4t + 3; 0 ≤ t ≤ 4
20
-5
5
-20
4
A) y = 4x2 + 3; 0 ≤ x ≤ 2
B) y = 3x2 + 4; -1 ≤ x ≤ 2
20
-5
20
5
-5
-20
-20
D) y = -3x2 + 19; 0 ≤ x ≤ 2
C) y = -3x + 19; 0 ≤ x ≤ 2
20
-5
5
20
5
-5
-20
5
-20
Simplify. Write your answers in the form of a+bi, where a and b are real numbers.
6 + 5i
11)
9 - 4i
A)
54 - 4 5 24 + 9 5
i
97
97
B)
54 - 4 5 24 - 9 5
i
+
97
97
C)
54 + 4 5 24 + 9 5
i
+
97
97
D)
54 - 4 5 24 + 9 5
i
+
97
97
Solve the exponential equation.
1
12) 3 x2 + 3 x =
9
A) -1 , 2
B) 1 , 2
C) -1 , -2
D) 1 , -2
B) (-2, 2, -5)
C) (-2, -5, 2)
D) (-5, 2, -2)
Solve the following system.
13) x + y + z = -5
x - y + 4z = -15
3x + y + z = -15
A) No solution
5
Solve the logarithmic equation.
14) log6 (4x - 5) = 1
A)
11
4
B)
log61 + 5
4
C)
11
6
D) 7
Solve using the elimination method.
15) -6x + 8y = -56
-2x - 4y = 28
A) (-1, -6)
B) (0, -7)
C) (0, -6)
D) No solution
C)
D)
Solve.
16) z 4 - 8z 2 + 12 = 0
A) ± 6, ± 2
B)
-6,
2
6,
2
-6,
-2
17) ∣8x - 3∣ ≥ 4
A) -∞, -
18)
7
∪ [4, ∞)
8
B) -
1 7
,
8 8
7
C) [ , ∞)
8
D) -∞, -
C) -25, -16
D) ± 20
1
7
∪ ,∞
8
8
x = 20 - x
A) ±9
B) 16
Solve. Use the REGRESSION feature on a graphing calculator.
19) In an art class, students were tested at the end of the course on a final exam. Then they were retested with an
equivalent test at subsequent time intervals. Their scores after time x, in months, are given in the following
table.
TIME, x
(IN MONTHS)
1
2
3
4
5
6
SCORE, y
85.1
84.8
84.6
84.4
84.3
84.1
Use a graphing calculator to fit a logarithmic function y = a + b ln x to the data. After how long will the test
scores fall below 83%?
A) y = 85.1435399 + 0.54128341 ln x; 332.8 months
B) y = 85.1435399 - 0.54128341 ln x; 1.4 months
C) y = 85.1435399 - 0.54128341 ln x; 52.5 months
D) y = 85.1435399 + 0.54128341 ln x; 52.5 months
Use the quadratic formula to find the exact solution.
20) x2 + 8x = -12
A) -2, 6
C) 2, -6
B) 2, 6
6
D) -2, -6
Answer Key
Testname: DEPT171FINALVERSION3
1) D
2) C
3) A
4) A
5) B
6) A
7) D
8) A
9) C
10) A
11) D
12) C
13) D
14) A
15) B
16) A
17) D
18) B
19) C
20) D
7