Test #1 Quick Quiz
The Quick quizzes are mostly concept quizzes. Doing only the Quick quizzes will not be
enough to learn the material and pass the test. The quizzes are no calculator. The Quick
quizzes are self-assessment quizzes, and they will not be collected or graded. The answer
for all quizzes are at the end of each quiz.
Section 1.1 Quick Quiz
Answer the following multiple choice questions by circling the correct response.
1. The function f (x) = x3 − x is defined for
(a) {x: x ≥ 0}
(c) {x: −∞ < x < ∞}.
(b) {x: x < 0}
2. The range of y = f (x) = x3 − x is
(a) {y: y ≥ 1}
(b) {y: −∞ < y < ∞}
(c) {y: y < 0}.
3. The function f (x) =√9 − 𝑥 2 is defined for
(a) {x: |x| > 3}
(c) {x : |x| ≤ 3}.
(b) {x : |x| < 3}
4. The graph of the function f (x) = −3x + 8 is
(a) a line with slope 8 and y-intercept (0, −3).
(b) a line with slope 3 and y-intercept (0, 8).
(c) a line with slope −3 and y-intercept (0, 8).
5. Suppose the height of a soccer ball that is kicked from the ground at time t = 0 is
h(t) = −5t2 + 60t (in feet). An appropriate domain for this problem is
(a) {t: 0 ≤ t ≤ 12}
(b) {t: 0 ≤ t ≤ 6}
(c) {t: −∞ < t < ∞}.
6. If f (x) = √𝑥 and g(x) = 1/ (x +1), then f (g(x)) is
(a)
1
.
√𝑥+1
(b)
1
√𝑥+1
(c) √𝑥 + 1
7. If f (x) = x3− x and g(x) = x−2, then g(f (x)) is
(a) x−6 − x−2
(b) (x3 − x) −2
(c) x6 − x2.
8. Suppose f (1) = 3, f (3) = 1, g(1) = 1, and g(3) = 3. Then f (g(3))
(a) equals 1
(b) equals 3
(c) cannot be determined.
9. With f (x) = √𝑥 and g(x) = 4 − x2, the composition function (f ο g)(x) is defined for
(a) all real numbers
(b) {x : |x| ≥ 2}
(c) {x : |x| ≤ 2}.
10. The function h(x) = x4 − 3x +1
(a) is even
(b) is odd
(c) has no symmetry.
11. The function g(x) = x(x3 − x)−1
(a) is even.
(b) is odd.
(c) has no symmetry.
12. The curve described by the equation x2 − y4 = 1 is symmetric about the
(a) x-axis only.
(b) y-axis only.
(c) the origin.
Quick Quiz 1.1 Answers:
1c 2b 3c 4c 5a 6a 7b 8a 9c 10c 11a 12c
Section 1.2 Quick Quiz
Answer the following multiple choice questions by circling the correct response.
𝑥+1
1. The function 𝑓(𝑥) = 𝑥−2 is a
(a) polynomial
(b) rational function (c) transcendental function.
2. The function f (x) = 2x10 − 3x2 is a
(a) polynomial
(b) trigonometric function
(c) transcendental function.
3. The function 𝑓(𝑥) = √𝑥 − 1 − 3𝑥 −2 is a
(a) polynomial
(b) algebraic function
4. The graph of f (x) = 2x5
(a) lies in the first and second quadrants.
(b) lies in the second and fourth quadrants.
(c) has a point for every real number x.
(c) rational function.
5. The graph below best represents the function
(a) f (x) = √4 − 𝑥 2
1
(c) f (x) = √𝑥 2 − 4 .
(b) 𝑥 2 −4
6. The data in the table below is best represented by the function
(a) f (x) = √𝑥 +1
(b) f (x) = x2 – 3
(c) f (x) = x2 − x.
x
−2
−1
1
3
4
6
f
1
−2
−2
6
13
33
7. Suppose your car gets exactly 30 miles per gallon of gasoline and you start driving with 15
gallons in the tank. The number of gallons of gasoline left in the tank after driving x miles is
given by the function
(a) g(x) = 30 −15x
(b) g(x) = 15− 30x
𝑥
(c) g(x) = 15− 30 .
8. The value of f(0) for the piecewise linear function 𝑓(𝑥) = {
(a) 1
(b) 0
2𝑥 + 1 𝑖𝑓 𝑥 ≤ 0
is
−𝑥 𝑖𝑓 𝑥 > 0
(c) undefined.
9. The function that gives the slope of f in Question 8 is
(a) 𝑔(𝑥) = {
2 𝑖𝑓 𝑥 < 0
.
1 𝑖𝑓 𝑥 > 0
(b) 𝑔(𝑥) = {
2
−1
𝑖𝑓 𝑥 < 0
.
𝑖𝑓 𝑥 > 0
(c) 𝑔(𝑥) = {
1 𝑖𝑓 𝑥 < 0
0 𝑖𝑓 𝑥 > 0
10. The graph of g(x) = (x − 2)2 + 3 is obtained by shifting the graph of f (x) = x2
(a) left 2 units and up 3 units (b) right 2 units and up 3 units (c) right 3 units and up 2 units.
11. The graph of y = f (3x) is
(a) the graph of y = f (x) compressed horizontally by a factor of 3.
(b) the graph of y = f (x) stretched horizontally by a factor of 3.
(c) the graph of y = f (x) shifted horizontally by 3 units.
12. The graph of y = 3(x − 2)4 is the graph of y = x4
(a) stretched vertically by a factor of 3 and stretched horizontally by a factor of 2.
(b) stretched vertically by a factor of 3 and shifted horizontally 2 units to the right.
(c) stretched vertically by a factor of 2 and compressed horizontally by a factor of 2.
Quick Quiz 1.2 Answers:
1b 2a 3b 4c 5c 6b 7c 8a 9b 10b 11a 12b
Section 1.3 Quick Quiz
Answer the following multiple choice questions by circling the correct response.
1. The radian measure of an angle corresponding to one-eighth of a circle is
(a) π/3.
(b) π/4.
(c) π/6.
2. The value of tan 3π/4 is
(a) – √3
(c) −1.
(b)1
3. Among the zeros of the function y = cos 2θ are
(a) 0, ±π/2.
(b) ±π.
(c) ±π/4.
4. The function y = sec x/ 2 is undefined at
(a) x = ±π
(b) x = 0, π/2
(c) x = 0, ±2π.
5. Among the solutions of sin 2x = cos 2x are
(a) π/4.
(b) π/8.
(c) π/3.
6. The function f (x) = cos (π x/ 4) has a period of
(a) 4.
(b) 8.
(c) 16.
7. The maximum value of the function f (x) = 4cos x +1 is
(a) 4.
(b) 6.
(c) 5.
8. The function f (x) = tan x has a period of
(b) π.
(a) 2π.
(c) tan x is not a periodic function.
9. The range of f (x) = sin x is
(a) [−π/2, π/2]
(b) all real numbers
(c) [−1, 1].
10. The domain of f (x) = cot x is
(a) {x : x ≠ 2nπ }
(b) all real numbers (c) {x : x ≠ nπ } .
Quick Quiz 1.3 Answers:
1b 2c 3c 4a 5b 6b 7c 8b 9c 10c
Section 2.1 Quick Quiz
Answer the following multiple choice questions by circling the correct response.
1. The position of an object moving along a line is given by the function s(t) = t2 − 2t.What is the
average velocity over the interval [0, 2]?
(a) 0
(b) 2
(c) –2
2. The position of an object moving along a line is s(t) = 2sin t. What is the average velocity over
the interval [0, π/2]?
(a) 2/π
(b) –2/π
(c) 4/π
3. The position of an object moving along a line is s(t) = t2 − 2t. What is the instantaneous
velocity at the point t = 1?
(a) 1
(b) 0
(c) –1
4. The position of an object moving along a line is s(t) = 2sin t. Which of the following values
best approximates the instantaneous velocity at t = 0?
(a) 2
(b) –2
(c) 2/π
5. Consider the graph of y = x3. Find the slope of the secant line between the points
corresponding to x = –1 and x = 1.
(a) 1
(b) 0
(c) –1
6. Which of the following values is the best approximation to the slope of the line tangent to the
graph of y = x3 at x = 0?
(a) 0
(c) –2
(b) 3
Quick Quiz 2.1 Answers:
1a 2c 3b 4a 5a 6a
Section 2.2 Quick Quiz
Answer the following multiple choice questions by circling the correct response.
1. If f(x) approaches 8 as x approaches 5 from the left, then you can be certain that
(a) lim+ 𝑓(𝑥) = 8.
(b) lim− 𝑓(𝑥) = 8.
(c) lim 𝑓(𝑥) = 8
𝑥→5
𝑥→5
𝑥→5
2. If lim− 𝑓(𝑥) = 5, lim+ 𝑓(𝑥) = 5 and f(2) = 6, then
𝑥→2
𝑥→2
(a) lim 𝑓(𝑥) = 5
(b) lim 𝑓(𝑥) = 6
𝑥→2
(c) lim 𝑓(𝑥) does not exist.
𝑥→2
𝑥→2
3. If lim 𝑓(𝑥) = 5 then
𝑥→2
(a) f (2) = 5
(b) f (2) is undefined.
(c) not enough information is given to determine f (2).
4. If f (2) = 5, then
(a) lim 𝑓(𝑥) = 5.
(b) lim 𝑓(𝑥) ≠ 5.
𝑥→2
𝑥→2
(c) not enough information is given to determine lim 𝑓(𝑥)
x→2
5. If lim− 𝑓(𝑥) = 6 and lim+ 𝑓(𝑥) = 7, then
x→1
(a) lim 𝑓(𝑥) = 6.
𝑥→1
x→1
(b) lim 𝑓(𝑥) = 7.
(c) lim 𝑓(𝑥) does not exist.
𝑥→1
𝑥→1
6. The values f (0.1) = 7.9, f (0.01) = 7.99, f (.001) = 7.999, and f (.0001) = 7.9999 lead us to
conjecture that
(a) lim− 𝑓(𝑥) = 8.
(b) lim+ 𝑓(𝑥) = 8. (c) lim 𝑓(𝑥) = 8.
𝑥→0
𝑥→0
Refer to the accompanying figure for Exercises 7–10.
𝑥→0
7. lim− 𝑔(𝑥) =
x→2
(a) 1.
(b) 3.
(c) 4.
(b) 3.
(c) 4.
(b) equals 4.
(c) does not exist.
(b) equals 5.
(c) does not exist.
8. lim+ 𝑔(𝑥) =
x→2
(a) 1.
9. lim 𝑔(𝑥)
x→2
(a) equals 1.
10. lim 𝑔(𝑥)
x→5
(a) equals 1.
Quick Quiz 2.2 Answers:
1b 2a 3c 4c 5c 6b 7c 8a 9c 10b
Section 2.3 Quick Quiz
Answer the following multiple choice questions by circling the correct response.
1. The limit lim
𝑥 2 −4𝑥+3
𝑥→3
𝑥−3
(a) does not exist.
(b) cannot be determined.
(c) equals 2.
2. If f(x) = g(x) for all values of x except possibly for x = 2 and lim 𝑔(𝑥) = 5, then
x→2
(a) f(2) = 5.
3. If 𝑓(𝑥) = {
(a) b = 0.
4. If 𝑓(𝑥) = {
(b) lim 𝑓(𝑥) may not equal 5.
x→2
x→2
4𝑥 + 1 𝑖𝑓 𝑥 ≠ 0
and lim 𝑓(𝑥) = 𝑓(0), then
𝑥 + 𝑏 𝑖𝑓 𝑥 = 0
x→0
(b) the value of b cannot be determined.
(c) b = 1.
4 𝑖𝑓 𝑥 ≠ 2
, then
5 𝑖𝑓 𝑥 = 2
(a) lim 𝑓(𝑥) = 5.
𝑥→2
(c) lim 𝑓(𝑥) = 5
(b) lim 𝑓(𝑥) = 4.
𝑥→2
(c) lim 𝑓(𝑥)does not exist.
𝑥→2
5. If f (5) does not exist, then lim 𝑓(𝑥)
x→5
(a) equals 5.
(b) does not exist.
(c) might exist.
6. If f (5) = 0, then lim 𝑓(𝑥)
𝑥→5
(a) equals 5.
7. If 𝑓(𝑥) = {
(b) might not exist.
(c) equals 0.
𝑔(𝑥) 𝑖𝑓 𝑥 < 0
and lim 𝑔(𝑥) = 2, then
5
𝑖𝑓 𝑥 ≥ 0
x→0
(a) lim+ 𝑓(𝑥) = 2.
𝑥→0
(b) lim+ 𝑓(𝑥) = 5.
𝑥→0
(c) lim+ 𝑓(𝑥)exists, but its precise value cannot be
𝑥→0
determined.
8. If −4x +12 ≤ 𝑔(𝑥)≤ 8− x2 for all x, then
(a) lim 𝑔(𝑥) = 4
x→2
(b) lim 𝑔(𝑥)exists, but its precise value cannot be determined.
x→2
(c) lim 𝑔(𝑥) does not exist.
x→2
9. If p is a polynomial, then lim 𝑝
x→𝑎
(a) may not exist.
(b) equals a.
(c) equals p(a).
10. If 𝑓(𝑥) = √𝑥 2 − 4, then
(a) lim− 𝑓(𝑥) exists, but lim 𝑓(𝑥) does not exist.
x→2
x→2
(b) lim+ 𝑓(𝑥) exists, but lim 𝑓(𝑥) does not exist.
x→2
x→2
(c) lim 𝑓(𝑥) exists.
x→2
Quick Quiz 2.3 Answers:
1c 2c 3c 4b 5c 6b 7b 8a 9c 10b
Section 2.4 Quick Quiz
Answer the following multiple choice questions by circling the correct response.
1. Which of the following statements is false if lim+ 𝑓(𝑥) = ∞?
x→a
(a) As 𝑥 → a+ , f (x) gets closer to the real number ∞.
(b) The values of f grow arbitrarily large as x approaches ‘a’ from the right.
(c) The line x = a is a vertical asymptote of f (x).
2. If f (1.1) = −500, f (1.01) = −5000, f (1.001) = −50000, f (1.0001) = −500000 and so forth, then
the most plausible conclusion is that
(a) lim+ 𝑓(𝑥) = −∞.
(b) lim+ 𝑓(𝑥) = ∞.
𝑥→1
(c) lim 𝑓(𝑥) = −∞
𝑥→−1
𝑥→1
Figure for Exercises 3 and 4
3. For the function y = g(x) in the above figure,
(a) lim+ 𝑔(𝑥) = ∞ .
(b) lim+ 𝑔(𝑥) = 0.
𝑥→1
(c) lim+ 𝑔(𝑥) = −∞.
𝑥→1
𝑥→1
4. For the function y = g(x) in the above figure,
(a) lim− 𝑔(𝑥) = ∞.
(b) lim− 𝑔(𝑥) = 0.
𝑥→1
(c) lim− 𝑔(𝑥) = −∞.
𝑥→1
𝑥→1
5. If lim 𝑓(𝑥) = 10 and lim 𝑔(𝑥) = 0, then
𝑥→1
x→1
𝑓(𝑥)
𝑓(𝑥)
(a) lim [𝑔(𝑥)]2 = 0.
𝑓(𝑥)
(b) lim [𝑔(𝑥)]2 = −∞. (c) lim [𝑔(𝑥)]2 = ∞.
𝑥→1
𝑥→1
𝑥→1
6. Suppose g(x) is negative and approaches 0 as x approaches 5. Then
1
1
(a) lim 𝑔(𝑥) = ∞.
1
(b) lim 𝑔(𝑥) = 0.
𝑥→5
(c) lim 𝑔(𝑥) = −∞.
𝑥→5
𝑥→5
7. As x → 3–, suppose f(x) → –5, g(x) → 2, and h(x) is negative and approaches 0. Then
(a) lim−
𝑥→3
8. lim
𝑓(𝑥)𝑔(𝑥)
= ∞.
ℎ(𝑥)
(b) lim−
𝑥→3
𝑓(𝑥)𝑔(𝑥)
ℎ(𝑥)
= −∞.
(𝑥−3)(𝑥+1)
𝑥→1
(𝑥−1)2
equals
(a) −∞.
Quick Quiz 2.4 Answers:
1a 2a 3c 4a 5c 6c 7a 8a
Section 2.5 Quick Quiz
(b) ∞.
(c) 0.
(c) lim−
𝑥→3
𝑓(𝑥)𝑔(𝑥)
ℎ(𝑥)
= 0.
Answer the following multiple choice questions by circling the correct response.
1. If (10) 4.9, (f = f 100) = 4.99, f (1000) = 4.999, f (10000) = 4.9999 and so forth, then the most
plausible conclusion is that
(a) lim 𝑓(𝑥) = ∞.
(b) lim 𝑓(𝑥) = 5.
𝑥→5
(c) lim 𝑓(𝑥) = 5.
𝑥→∞
𝑥→−∞
2𝑥
2. Evaluate lim
𝑥→∞ 𝑥+1
(a) 2
(b) ½
3. Evaluate lim
(c) 0
2𝑥
𝑥→∞ (𝑥+1)2
(a) 2
(b) ½
(c) 0
4. As x →∞, suppose f (x) →5, g(x) →−2, and h(x) →∞. Then
(a) lim
𝑥→∞
(b) lim
𝑓(𝑥)𝑔(𝑥)
𝑥→∞ ℎ(𝑥)
𝑓(𝑥)𝑔(𝑥)
(c) lim
𝑥→∞
=∞
ℎ(𝑥)
𝑓(𝑥)𝑔(𝑥)
ℎ(𝑥)
= −∞
=0
𝑥2
5. The vertical and horizontal asymptotes of 𝑓(𝑥) = 2𝑥+1
(a) x = −½ and y = ½
(b) ) x = −½ and no horizontal asymptote.
(c) no vertical asymptote and y = ½
6. Evaluate lim
3−𝑥
𝑥→∞ 2𝑥 2 +5
(a) 0
(b) ∞
(c) 2
7. Evaluate lim (𝑥 + sin(𝑥))
𝑥→∞
(a) 0
(b) ∞
(c) ln 2
𝑥
8. The end behavior of the function 𝑓(𝑥) = √𝑥 2
+1
may be summarized as follows: f has
(a) no horizontal asymptotes. (b) one horizontal asymptote. (c) two horizontal asymptotes.
1200𝑡 2
9. The population of a culture of bacteria is given by 𝑝(𝑡) = 2𝑡 2 +100. What can you conclude?
(a) The population grows without bound.
(b) The population reaches a steady state level of 0.
(c) The population reaches a steady state level of 600.
10. As x →∞, the function f (x) = sin x / x
(a) approaches 1
(b) approaches 0
(c) grows without bound.
Quick Quiz 2.5 Answers:
1b 2a 3c 4c 5b 6a 7b 8c 9c 10b
Section 2.6 Quick Quiz
Answer the following multiple choice questions by circling the correct response.
1. The graph of y = f(x) is continuous on
(a) [0,1].
(b) [0,1).
(c) (0,1].
2. The graph of y = f(x) is continuous on
(a) (1, 2).
(b) [1, 2).
(c) (1, 2].
3. The graph of y = f(x) is continuous on
(a) (3,5].
(b) [3,5].
(c) [3,5).
Figure for Exercises 1–3
4. If lim− 𝑓(𝑥) = 4, lim+ 𝑓(𝑥) = 5, and 𝑓(2) = 5, then 𝑓is continuous
𝑥→2
(a) at x = 2.
𝑥→2
(b) from the left at x = 2.
5. The function 𝑓(𝑥) =
(a) −1.
6. If 𝑓(𝑥) = {
𝑥
𝑥 2 −1
(c) from the right at x = 2.
is continuous for all values of x except
(b) 1.
(c) –1 and 1.
2𝑥
𝑖𝑓 𝑥 < 1
, then f is continuous
3𝑥 − 2 𝑖𝑓 𝑥 ≥ 1
(a) at x = 1. (b) from the left at x = 1. (c) from the right at x = 1.
7. If 𝑓(𝑥) = {
2𝑥
𝑎
(a) a = 2.
𝑖𝑓 𝑥 < 1
, then f is continuous at x = 1 if
𝑖𝑓 𝑥 ≥ 1
(b) a = 1.
(c) a = 3.
8. If lim− 𝑓(𝑥) = 10, lim+ 𝑓(𝑥) = 12, and is continuous from the right at x = 5, then
𝑥→5
𝑥→5
(a) f(5) = 10.
(b) f(5) = 12.
(c) f(5) is undefined.
9. The largest interval on which the function √25 − 𝑥 2 is continuous is
(a) [–10, 10]. (b) [–5,0]. (c) [–5,5].
10. Which of the following functions is continuous for all values of x?
(a) √3𝑥 2 − 2 .
Quick Quiz 2.6 Answers:
1b 2a 3c 4c 5c 6c 7a 8b 9c 10c
5x
(b) |𝑥 8 −1| .
5x
(c) 𝑥 8 +1.