6 Drill Questions: Basic Functions

At any point, you can submit your answers by collecting them and uploading them to the class site.

No answers yet collected

Link to upload site

If requested by your instructor, please identify here the people from whom you received assistance on this assignment.

If the answers that have been loaded automatically are not yours, press this button before starting your work:

Drill 6. 1 Which storybook functions produce output 1 when the input is zero?

psp-1-32do

hillside() & flat()

flat() & double()

flat() & doublings()

osc() & flat()

Drill 6. 2 Some storybook functions have a bounded output, that is, the output has finite maximum and minimum values. Pick the one that does not fit into this category.

lhb-1-k32
osc()       hill()       hillside()       double()       flat()      

Drill 6. 3 For which storybook functions is the output bounded on the bottom by zero but unbounded on the top?

arf-1-82kd

doublings() & steady()

hillside() & hill()

double() & recip()

steady() & osc()

Drill 6. 4 Which storybook functions have an output that is unbounded on both the top and the bottom?

sts-1-3cw

doublings() & steady()

hillside() & hill()

double() & recip()

steady() & osc()

Drill 6. 5 Which storybook function has an output bounded by -1 and 1?

gsl-1-cjs

hillside()

osc()

doublings()

steady()

Drill 6. 6 Which storybook function has an output bounded by 0 and 1?

slk-1-cjs

hillside()

osc()

doublings()

steady()

Drill 6. 7 Which of the following is not the name of a storybook function?

d06-tbs-2da
hill()       ramp()       steady()       doublings()       recip()      

Drill 6. 8 Match each storybook function to its characteristic behavior. The function osc() …

d06-sbg-932

goes up and then back down to a baseline

repeats the same pattern over and over

starts low and levels off at a high value

increases by the same factor for each unit increase in input

Drill 6. 9 The function hillside() …

d06-frm-clw

goes up and then back down to a baseline

repeats the same pattern over and over

starts at a low value and gradually levels off at a higher value

decreases quickly at first, then more slowly

Drill 6. 10 The function hill() …

d06-rts-qclw

goes up from a baseline and then back down to the baseline

repeats the same pattern over and over

starts at a low value and gradually levels off at a higher value

increases by the same factor for each unit increase in input

Drill 6. 11 The function double() …

d06-mml-ldx

goes up from a baseline and then back down to the baseline

the output doubles for every unit increase in input

tells you how many doublings correspond to a given output

decreases quickly at first, then more slowly

Drill 6. 12 The function doublings() is closely related to double(). What is the relationship?

d06-gtb-ekx

They are the same function with different names

doublings() tells you the input needed to reach a given output from double()

doublings() is double() multiplied by 2

doublings() is the rate of change of double()

Drill 6. 13 Which storybook function would best describe the outdoor temperature over the course of a single day (rising in the morning, falling in the evening, repeating daily)?

d06-scb-daily
hill()       hillside()       osc()       double()      

Drill 6. 14 Which storybook function would best describe the adoption of a new technology (few users at first, rapid growth, then leveling off as the market saturates)?

d06-blk-73
hill()       hillside()       osc()       double()      

Drill 6. 15 Which storybook functions have a positive rate of change for all positive inputs?

recip()   d06-str-3ks
True     or       False      

double()   d06-str-lxe
True     or       False      

hill()   d06-str-8ue
True     or       False      

hillside()   d06-str-lex
True     or       False      

steady()   d06-str-cwox
True     or       False      

Drill 6. 16 For the osc() function, what is the period (the input interval over which the function completes one full cycle and returns to its starting pattern)?

d06-gkh-ekos
0.5       1       2       3.14159      

Drill 6. 17 At what input value does hillside() produce an output of 0.5 (halfway between its minimum and maximum)?

d06-blb-ckw
-1       0       0.5       1      

Drill 6. 18 For the double() function:

  1. What is the output when the input is 0?
d06-bir-zero
0       0.5       1       2       4      

  1. What is the output when the input is 3?
d06-bir-three
3       6       8       9      

  1. What is the output when the input is -1?
d06-bir-neg
-2       -1       0.5       1      

Drill 6. 19 For the doublings() function:

  1. What is the output when the input is 8?
d06-swj-8
2       3       4       8       16      

  1. What is the output when the input is 1?
d06-swj-1
-1       0       1       2      

  1. What input to doublings() gives an output of -2?
d06-swj-neg2
-4       -2       0.25       0.5      

Drill 6. 20 The flat() function always returns the same output regardless of input. What is the rate of change of flat() with respect to its input?

d06-fbs-4kdi
-1       0       1       It depends on the input.      

Drill 6. 21 The storybook functions take pure numbers (dimensionless) as input and produce pure numbers as output. To use them with real-world quantities that have units, we use input transformations.

An input transformation has the form \(a(q - q_0)\) where \(q\) is the real-world input quantity. What must be true about the dimension of \(q_0\)?

d06-bsc-esd

It must be dimensionless

It must have the same dimension as \(q\)

It must have the reciprocal dimension of \(q\)

It can have any dimension

Drill 6. 22 In the input transformation \(a(q - q_0)\), what must be true about the dimension of parameter \(a\)?

d06-bsk-a

It must be dimensionless

It must have the same dimension as \(q\)

It must have dimension \(1/[q]\) (the reciprocal of \(q\)’s dimension)

It can have any dimension

Drill 6. 23 Suppose you want to model oil production using hillside(), and the data shows production reached half its maximum value around the year 1970. In the input transformation \(a(\text{year} - q_0)\), what value should \(q_0\) have?

d06-khb-oil
0       0.5       1970       2023      

Drill 6. 24 An output transformation has the form \(A \cdot f(\text{input}) + B\) where \(f()\) is a storybook function. If you want the transformed function to have a maximum output of 100 and a minimum of 0, and the storybook function naturally ranges from 0 to 1, what should \(A\) be?

d06-ahs-A-ues
1       50       100       200      

Continuing from the previous question, what should \(B\) be?

d06-ahs-B-3xl
-50       0       50       100      

Drill 6. 25 If a quantity is measured in miles per gallon and you need to create a dimensionless input for a storybook function using the transformation \(a(q - q_0)\), what are the units of parameter \(a\)?

d06-pcs-1

miles per gallon

gallons per mile

dimensionless

miles

Drill 6. 26 The graph shows one of the storybook functions but with either input scaling, output scaling, or none.

elr-1-kre
input scaling       output scaling       none      

Drill 6. 27 The graph shows one of the storybook functions but with either input scaling, output scaling, or none.

ksr-1-ese
input scaling       output scaling       none      

Drill 6. 28 The graph shows one of the storybook functions but with either input scaling, output scaling, or none.

shf-1-ese
input scaling       output scaling       none      

Drill 6. 29 The graph shows one of the storybook functions but with either input scaling, output scaling, or none.

psk-1-ese
input scaling       output scaling       none      

Drill 6. 30  

Which storybook function does this graph show?

sdp-1-dkw
hill()       hillside()       osc()       double()      

Drill 6. 31  

Which storybook function does this graph show?

psc-1-xkd
hill()       hillside()       osc()       recip()      

Drill 6. 32  

Which storybook function does this graph show?

blp-1-xlde
doublings()       double()       steady()       hillside()      

Drill 6. 33  

Which storybook function does this graph show?

tdp-1-lfr
hill()       hillside()       osc()       steady()      

Drill 6. 34  

Which storybook function does this graph show?

ntg-1-cdwq
doublings()       double()       recip()       hillside()