Sem 2 Final Practice Problems
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the average rate of change of the function over the given interval.
1) f(x) = 6x 3 + 2x2 + 4, [-3, 5] 1)
804 201 944
A) B) 118 C) D)
5 2 5
2) f(x) = 8 + cos x, [0, π] 2)
2 1 8
A) - ≈ -0.637 B) 0 C) ≈ 0.318 D) ≈ 2.546
π π π
Find the slope of the line tangent to the curve at the given value of x.
3) f(x) = -2x2 + 6x; x = 6 3)
A) -108 B) -3 C) 12 D) -18
Solve the problem.
4) The equation for free fall at the surface of Planet X is s = 8.76t2 m with t in seconds. Assume a rock 4)
is dropped from the top of a 600m cliff. Find the speed of the rock at t = 5 sec.
A) 42.8 m/sec B) 43.8 m/sec C) 87.6 m/sec D) 88.6 m/sec
Solve by completing the square.
5) 4x2 + 35 = -24x 5)
5 7 -5 -7 -7 21 -5 -7
A) , B) , C) , D) ,
2 2 2 2 4 2 4 4
Write the product in standard form.
6) (2 + 7i)(4 - 3i) 6)
A) -21i2 + 22i + 8 B) 29 + 22i C) -13 + 34i D) 29 - 22i
Perform the indicated operation. Write the result in standard form.
7) (-2 + 3i)3 7)
A) 46 + 36i + i3 B) 8 - 54i2 + 36i + i3
C) 46 + 9i D) 46 + 107i
Find the product of the complex number and its conjugate.
8) -3 + 5i 8)
A) 35 B) -16 C) 37 D) 34
Write the expression in standard form.
9 + 2i
9) 9)
3 - 6i
1 4 13 4 1 4
A) - + i B) - + i C) + i D) 13 + 16i
27 27 9 27 3 3
1
,Determine the intervals on which the function is increasing, decreasing, and constant.
10) 10)
y
5
4
3
2
1
-5 -4 -3 -2 -1-1 1 2 3 4 5 x
-2
-3
-4
-5
A) Increasing on (-2, 0) and (3, 5); Decreasing on (1, 3); Constant on (-5, -2)
B) Increasing on (-1, 0) and (3, 5); Decreasing on (0, 3); Constant on (-5, -3)
C) Increasing on (-2, 0) and (3, 4); Decreasing on (-5, -2) and (1, 3)
D) Increasing on (1, 3); Decreasing on (-2, 0) and (3, 5); Constant on (2, 5)
Identify intervals on which the function is increasing, decreasing, or constant.
11) f(x) = x3 - x 2 + 2 11)
A) Increasing: (0, 0.67); decreasing: (- ∞, 0) and (0.67, ∞)
B) Increasing: (- ∞, 0) and (0.67, ∞); constant: (0, 0.67)
C) Increasing: (- ∞, -2) and (2, ∞); decreasing: (-2, 2)
D) Increasing: (- ∞, 0) and (0.67, ∞); decreasing: (0, 0.67)
Determine algebraically whether the function is even, odd, or neither even nor odd.
12) f(x) = 3x 2 - 1 12)
A) Neither B) Even C) Odd
13) f(x) = -9x3 + 8x 13)
A) Even B) Neither C) Odd
14) f(x) = -9x4 + 5x + 3 14)
A) Even B) Neither C) Odd
Find the asymptote(s) of the given function.
x-1
15) f(x) = vertical asymptotes(s) 15)
x2 + 2
A) x = 1, x = -1 B) None C) x = -2 D) x = 2
(x - 3)(x + 1)
16) h(x) = vertical asymptotes(s) 16)
x2 - 1
A) x = 1, x = -1 B) x = -3, x = 1 C) x = 3, x = -1 D) None
24x2
17) h(x) = horizontal asymptotes(s) 17)
8x2 - 6
A) None B) y = 6 C) y = 3 D) y = 6
2
, 18) f(x) = 1.1x horizontal asymptotes(s) 18)
A) None B) y = 1.1 C) x = 0 D) y = 0
Find the (x,y) pair for the value of the parameter.
19) x = 6t - 2 and y = 15 - t for t =-1 19)
A) (-8, 16) B) (-6, 1) C) (-6, 15) D) (16, -8)
Give the equation of the function g whose graph is described.
3
20) The graph of f(x) = x is shifted 7.3 units to the left. This graph is then vertically stretched by a 20)
factor of 3.0. Finally, the graph is reflected across the x-axis.
3 3
A) g(x) = -3.0 x - 7.3 B) g(x) = -7.3 x + 3.0
3 3
C) g(x) = 3.0 x + 7.3 D) g(x) = -3.0 x + 7.3
21) The graph of f(x) = x2 - 4x + 3 is horizontally shrunk by a factor of 1/4 . 21)
1 3
A) g(x) = x2 - x + B) g(x) = 4x 2 - 16 x + 12
4 4
1 2
C) g(x) = x - x+3 D) g(x) = 4x 2 - 16 x + 3
16
Fill in the blanks to complete the statement.
22) The graph of y = - x + 2 can be obtained from the graph of y = x by shifting horizontally ? 22)
units to the ? and reflecting across the ? -axis.
A) 2; left; x B) 2; left; y C) 2; right; x D) -2; left; x
3 3
23) The graph of y = -0.1 -x can be obtained from the graph of y = x by reflecting across the ? 23)
-axis, shrinking vertically by a factor of ? , and then reflecting across the ? -axis.
A) x; -0.1; y B) x; 0.1; x C) y; -0.1; x D) y; 0.1; x
Determine a formula for the exponential function.
24) The indicated point is (0, e2 ). Which of the following is the correct equation of the function? 24)
y
10
5
-10 -5 5 10 x
-5
-10
A) y = ex + 2 B) y = ex - 2 C) y = ex + 2 D) y = ex - 2
3
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the average rate of change of the function over the given interval.
1) f(x) = 6x 3 + 2x2 + 4, [-3, 5] 1)
804 201 944
A) B) 118 C) D)
5 2 5
2) f(x) = 8 + cos x, [0, π] 2)
2 1 8
A) - ≈ -0.637 B) 0 C) ≈ 0.318 D) ≈ 2.546
π π π
Find the slope of the line tangent to the curve at the given value of x.
3) f(x) = -2x2 + 6x; x = 6 3)
A) -108 B) -3 C) 12 D) -18
Solve the problem.
4) The equation for free fall at the surface of Planet X is s = 8.76t2 m with t in seconds. Assume a rock 4)
is dropped from the top of a 600m cliff. Find the speed of the rock at t = 5 sec.
A) 42.8 m/sec B) 43.8 m/sec C) 87.6 m/sec D) 88.6 m/sec
Solve by completing the square.
5) 4x2 + 35 = -24x 5)
5 7 -5 -7 -7 21 -5 -7
A) , B) , C) , D) ,
2 2 2 2 4 2 4 4
Write the product in standard form.
6) (2 + 7i)(4 - 3i) 6)
A) -21i2 + 22i + 8 B) 29 + 22i C) -13 + 34i D) 29 - 22i
Perform the indicated operation. Write the result in standard form.
7) (-2 + 3i)3 7)
A) 46 + 36i + i3 B) 8 - 54i2 + 36i + i3
C) 46 + 9i D) 46 + 107i
Find the product of the complex number and its conjugate.
8) -3 + 5i 8)
A) 35 B) -16 C) 37 D) 34
Write the expression in standard form.
9 + 2i
9) 9)
3 - 6i
1 4 13 4 1 4
A) - + i B) - + i C) + i D) 13 + 16i
27 27 9 27 3 3
1
,Determine the intervals on which the function is increasing, decreasing, and constant.
10) 10)
y
5
4
3
2
1
-5 -4 -3 -2 -1-1 1 2 3 4 5 x
-2
-3
-4
-5
A) Increasing on (-2, 0) and (3, 5); Decreasing on (1, 3); Constant on (-5, -2)
B) Increasing on (-1, 0) and (3, 5); Decreasing on (0, 3); Constant on (-5, -3)
C) Increasing on (-2, 0) and (3, 4); Decreasing on (-5, -2) and (1, 3)
D) Increasing on (1, 3); Decreasing on (-2, 0) and (3, 5); Constant on (2, 5)
Identify intervals on which the function is increasing, decreasing, or constant.
11) f(x) = x3 - x 2 + 2 11)
A) Increasing: (0, 0.67); decreasing: (- ∞, 0) and (0.67, ∞)
B) Increasing: (- ∞, 0) and (0.67, ∞); constant: (0, 0.67)
C) Increasing: (- ∞, -2) and (2, ∞); decreasing: (-2, 2)
D) Increasing: (- ∞, 0) and (0.67, ∞); decreasing: (0, 0.67)
Determine algebraically whether the function is even, odd, or neither even nor odd.
12) f(x) = 3x 2 - 1 12)
A) Neither B) Even C) Odd
13) f(x) = -9x3 + 8x 13)
A) Even B) Neither C) Odd
14) f(x) = -9x4 + 5x + 3 14)
A) Even B) Neither C) Odd
Find the asymptote(s) of the given function.
x-1
15) f(x) = vertical asymptotes(s) 15)
x2 + 2
A) x = 1, x = -1 B) None C) x = -2 D) x = 2
(x - 3)(x + 1)
16) h(x) = vertical asymptotes(s) 16)
x2 - 1
A) x = 1, x = -1 B) x = -3, x = 1 C) x = 3, x = -1 D) None
24x2
17) h(x) = horizontal asymptotes(s) 17)
8x2 - 6
A) None B) y = 6 C) y = 3 D) y = 6
2
, 18) f(x) = 1.1x horizontal asymptotes(s) 18)
A) None B) y = 1.1 C) x = 0 D) y = 0
Find the (x,y) pair for the value of the parameter.
19) x = 6t - 2 and y = 15 - t for t =-1 19)
A) (-8, 16) B) (-6, 1) C) (-6, 15) D) (16, -8)
Give the equation of the function g whose graph is described.
3
20) The graph of f(x) = x is shifted 7.3 units to the left. This graph is then vertically stretched by a 20)
factor of 3.0. Finally, the graph is reflected across the x-axis.
3 3
A) g(x) = -3.0 x - 7.3 B) g(x) = -7.3 x + 3.0
3 3
C) g(x) = 3.0 x + 7.3 D) g(x) = -3.0 x + 7.3
21) The graph of f(x) = x2 - 4x + 3 is horizontally shrunk by a factor of 1/4 . 21)
1 3
A) g(x) = x2 - x + B) g(x) = 4x 2 - 16 x + 12
4 4
1 2
C) g(x) = x - x+3 D) g(x) = 4x 2 - 16 x + 3
16
Fill in the blanks to complete the statement.
22) The graph of y = - x + 2 can be obtained from the graph of y = x by shifting horizontally ? 22)
units to the ? and reflecting across the ? -axis.
A) 2; left; x B) 2; left; y C) 2; right; x D) -2; left; x
3 3
23) The graph of y = -0.1 -x can be obtained from the graph of y = x by reflecting across the ? 23)
-axis, shrinking vertically by a factor of ? , and then reflecting across the ? -axis.
A) x; -0.1; y B) x; 0.1; x C) y; -0.1; x D) y; 0.1; x
Determine a formula for the exponential function.
24) The indicated point is (0, e2 ). Which of the following is the correct equation of the function? 24)
y
10
5
-10 -5 5 10 x
-5
-10
A) y = ex + 2 B) y = ex - 2 C) y = ex + 2 D) y = ex - 2
3
