Chap 6 Review

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

-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 $f(x)\equiv 2x+1$

-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 $f(x)\equiv 2x+1$

-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 $f(x)\equiv 2x+1$

-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 $f(x)\equiv 2x+1$

-2       -4       2       4       9      

question id: drill-M01-8

Exercise 6 What is the rate of change of the function $f(x)\equiv 3x-2$ 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 $f(x)\equiv 3x-2$ 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 $$f(x)\equiv 3x-2$$ 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 $g(x)\equiv 2-3x+4x^3?$

Polynomial       Discontinuous       Periodic       Power-law      

question id: drill-M03-6

Figure 1: .

Exercise 11 Which of the functions in Figure 1 is concave up over the domain shown covered by the x-axis?

A       B       C      

question id: drill-M03-12

Figure 2: .

Exercise 12 Which of these functions in Figure 2 has a vertical asymptote?

A       B       C      

question id: drill-M03-13

Figure 3: .

Exercise 13 Which of the functions in Figure 3 has a vertical asymptote?

A       B       C      

question id: drill-M03-14

Figure 4: .

Exercise 14 For the function in Figure 4, where is the horizontal asymptote located?

At $x=0$       At $x=1$       At 20 as $x\to \pm \mathrm{\infty }$      

question id: drill-M03-18

Figure 5: .

Exercise 15 Does the function in Figure 5 have an inflection point?

yes       no       cannot tell      

question id: drill-M03-16

Figure 6: .

Exercise 16 Does the function in Figure 6 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 7?

At 2 as $x\to \pm \mathrm{\infty }$

At 2 as $x\to -\mathrm{\infty }$

At 6 as $x\to -\mathrm{\infty }$

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 7?

At 2 as $x\to \pm \mathrm{\infty }$

At 2 as $x\to \mathrm{\infty }$

At 6 as $x\to \mathrm{\infty }$

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 1?

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 9?

$t=-2.5$       $t=-1.25$       $t=0$       $t=1.25$       $t=2.5$      

question id: drill-Quiz-2-4

Exercise 21 Which of these is an argmax of the function in Figure 9?

$t=-2.5$       $t=-1.25$       $t=0$       $t=1.25$       $t=2.5$      

question id: drill-Quiz-2-3

Figure 10: .

Exercise 22 According to Figure 10, 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 10, 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 10, 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 11, which of these properties does not apply?

discontinuous

monotonic

concave-down

no inflection point

question id: drill-Quiz-1-17

Figure 12: A periodic function

Exercise 26 What’s the period of the function graphed in Figure 12?

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.

1

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

True       False      

question id: drill-hlbv-1

Exercise 29 The function $g(x)\equiv e^x$ has an inflection point on the domain $-\mathrm{\infty }<x<\mathrm{\infty }$.

True       False      

question id: drill-hlbv-2

Exercise 30 The function $g(x)\equiv e^x$ is monotonic on the domain $-\mathrm{\infty }<x<\mathrm{\infty }$.

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 $$0<x<\mathrm{\infty }$$. (You need only check in the interval $0<x\le 100.$)

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

2. True or false. A function can cross its horizontal asymptote.

True       False      

question id: seal-wake-bed-2

3. 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

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

True       False      

question id: seal-wake-bed-4

06-review.rmarkdown

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