Chap 6 Review

\[ \newcommand{\dnorm}{\text{dnorm}} \newcommand{\pnorm}{\text{pnorm}} \newcommand{\recip}{\text{recip}} \]

Exercise 1 What is the value of \(f(4)\) when \(f(x) \equiv 2 x + 1\ ?\)

-2       -4       2       4       9      

question id: drill-M01-4

Exercise 2 What is the change in the value of \(f()\) when the input goes from 2 to 4?
Assume \(f(x) \equiv 2 x + 1\)

-4       -2       2       4       9      

question id: drill-M01-5

Exercise 3 What is the rate of change in the value of \(f()\) when the input goes from 2 to 4?
Assume \(f(x) \equiv 2 x + 1\)

-2       -4       2       4       9      

question id: drill-M01-6

Exercise 4 What is the change in the value of \(f()\) when the input goes from 4 to 2?
Assume \(f(x) \equiv 2 x + 1\)

-2       -4       2       4       9      

question id: drill-M01-7

Exercise 5 What is the rate of change in the value of \(f()\) when the input goes from 4 to 2?
Assume \(f(x) \equiv 2 x + 1\)

-2       -4       2       4       9      

question id: drill-M01-8

Exercise 6 What is the rate of change of the function \(f(x) \equiv 3 x - 2\) when the input is 4?

-2       0.3       2       3       10      

question id: drill-M01-9

Exercise 7 What is the change in value of the function \(f(x) \equiv 3 x - 2\) as the input goes from 3 to 3.1?

-2       0.3       2       3       10      

question id: drill-M01-10

Exercise 8 What is the rate of change in value of the function \[f(x) \equiv 3 x - 2\] as the input goes from 3 to 3.1?

-2       0.3       2       3       10      

question id: drill-M01-11

Exercise 9 What is the period of the \(\sin()\) function?

1       \(2/\pi\)       \(\pi/2\)       \(\pi\)       \(2 \pi\)      

question id: drill-M03-2

Exercise 10 Which of these words is most appropriate to describe the function \(g(x) \equiv 2 - 3 x + 4x^3 ?\)

Polynomial       Discontinuous       Periodic       Power-law      

question id: drill-M03-6

Figure 1: .

Exercise 11 Which of the functions in Figure fig-m3-twelve is concave up over the domain shown in Figure fig-m3-twelve?

A       B       C      

question id: drill-M03-12

Figure 2: .

Exercise 12 Which of these functions in Figure fig-m3-fourteen has a vertical asymptote?

A       B       C      

question id: drill-M03-13

Figure 3: .

Exercise 13 Which of the functions in Figure fig-m3-fourteen-b has a vertical asymptote?

A       B       C      

question id: drill-M03-14

Figure 4: .

Exercise 14 For the function in Figure fig-m3-fourteen-c, where is the horizontal asymptote located?

At \(x=0\)       At \(x=1\)       At 20 as \(x \rightarrow \pm\infty\)      

question id: drill-M03-18

Figure 5: .

Exercise 15 Does the function in Figure fig-m3-twelve-b have an inflection point?

yes       no       cannot tell      

question id: drill-M03-16

Figure 6: .

Exercise 16 Does the function in Figure fig-m3-fourteen-d have an inflection point?

yes       no       cannot tell      

question id: drill-M03-17

Figure 7: .

Exercise 17 Which of these is a correct description of a horizontal asymptote in the function in Figure fig-m3-fourteen-e?

At 2 as \(x \rightarrow \pm\infty\)

At 2 as \(x \rightarrow -\infty\)

At 6 as \(x \rightarrow -\infty\)

There is no horizontal asymptote.

question id: drill-M03-19

Exercise 18 Which of these is a correct description of a horizontal asymptote in the function in Figure fig-m3-fourteen-e?

At 2 as \(x \rightarrow \pm\infty\)

At 2 as \(x \rightarrow \infty\)

At 6 as \(x \rightarrow \infty\)

There is no horizontal asymptote.

question id: drill-M03-20

Figure 8: .

Exercise 19 Which of these is the max of the function in Figure fig-rev2-03?

0       1       2       3       4      

question id: drill-Quiz-2-7

Figure 9: .

Exercise 20 Which of these is an argmin of the function in Figure fig-rev2-02b?

\(t = -2.5\)       \(t = -1.25\)       \(t = 0\)       \(t = 1.25\)       \(t = 2.5\)      

question id: drill-Quiz-2-4

Exercise 21 Which of these is an argmax of the function in Figure fig-rev2-02b?

\(t = -2.5\)       \(t = -1.25\)       \(t = 0\)       \(t = 1.25\)       \(t = 2.5\)      

question id: drill-Quiz-2-3

Figure 10: .

Exercise 22 According to Figure fig-quiz-1-argmax, which of these values is the argmax of the function?

0       1       2       3      

question id: drill-Quiz-1-14

Exercise 23 According to Figure fig-quiz-1-argmax, which of these values is the maximum of the function?

0       1       2       3      

question id: drill-Quiz-1-15

Exercise 24 For the function in Figure fig-quiz-1-argmax, which of these properties does not apply?

continuous

monotonic

concave-down

no inflection point

question id: drill-Quiz-1-16

Figure 11: .

Exercise 25 For the function in Figure fig-properties-1, which of these properties does not apply?

discontinuous

monotonic

concave-down

no inflection point

question id: drill-Quiz-1-17

Figure 12: .

Exercise 26 What’s the period of the sinusoid in Figure fig-rev2-03b?

1       2       3       4       5      

question id: drill-Quiz-2-22

Exercise 27 Which of these pattern-book functions has a discontinuity?

\(g(x) \equiv x^{-1}\)       \(g(x) \equiv - x^1\)       \(\text{dnorm}(x)\)       \(\sin(x)\)      

question id: drill-M03-1

Exercise 38 For each of the following, plot out the function over an appropriate graphics domain to determine whether the statement is true or false.

Exercise 28 The function \[f(t)\equiv \sin(t)\] has a local max of \[1\] somewhere on the domain \[-\infty < t < \infty\].

True       False      

question id: drill-hlbv-1

Exercise 29 The function \[g(x)\equiv e^x\] has an inflection point on the domain \[-\infty < x < \infty\].

True       False      

question id: drill-hlbv-2

Exercise 30 The function \[g(x)\equiv e^x\] is monotonic on the domain \[-\infty < x < \infty\].

True       False      

question id: drill-hlbv-3

Exercise 31 The function \[g(x)\equiv e^x\] has a vertical asymptote.

True       False      

question id: drill-hlbv-4

Exercise 32 The function \[h(x)\equiv \ln(x)\] has a vertical asymptote.

True       False      

question id: drill-hlbv-5

Exercise 33 The function \[h(x)\equiv \ln(x)\] has a horizontal asymptote.

True       False      

question id: drill-hlbv-6

Exercise 34 The function \[\text{inv}(val)\equiv 1/val\] has a vertical asymptote.

True       False      

question id: drill-hlbv-7

Exercise 35 The function \[\text{inv}(val)\equiv 1/val\] has a horizontal asymptote.

True       False      

question id: drill-hlbv-8

Exercise 36 The function \[f(x)\equiv 1/x\] is monotonically decreasing (i.e., monotonic AND decreasing) on the domain \[0<x<\infty\]. (You need only check in the interval \(0<x\leq 100.\))

True       False      

question id: drill-hlbv-9

Exercise 37 The function \[\text{inv}(val)\equiv 1/val\] is continuous.

True       False      

question id: drill-hlbv-10

Exercise 39  

  1. What is the maximum number of horizontal asymptotes that a function can have?
one       two       three       as many as you like      

question id: seal-wake-bed-1

  1. True or false. A function can cross its horizontal asymptote.
True       False      

question id: seal-wake-bed-2

  1. What is the maximum number of vertical asymptotes that a function can have?
one       two       three       as many as you like      

question id: seal-wake-bed-3

  1. True or false: A function can cross its vertical asymptote.
True       False      

question id: seal-wake-bed-4

No answers yet collected