Chap 2 Review

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Exercise 1 Which of these is the mathematical symbol for “is defined as”?

$=$       $\equiv$       $\sim$       $\approx$      

question id: M01-1

Exercise 2 What is the name of the function defined by $$f(y)\equiv \sin (y)+e^y?$$

$f$       $\sin$       $f(y)$      

question id: M01-2

Exercise 3 How do we refer to the output generated by applying $g(x)\equiv x+3$ to the input 3?

$g(x)$       $g(3)$       $y=6$      

question id: M01-3

Exercise 4 Using our notation conventions from the textbook, which one of the following kinds of things is $y_0?$

A constant       A function name       An input name      

question id: M03-22

Exercise 5 Using our notation conventions from the textbook, which one of the following kinds of things is $t^{\star }?$

A constant       A function name       An input name      

question id: M04-1

Exercise 6 Using our notation conventions from the textbook, which one of the following kinds of things is $B?$

A constant       A function name       An input name      

question id: M04-2

Exercise 7 Using our notation conventions from the textbook, which one of the following kinds of things is $F()?$

A constant       A function name       An input name      

question id: MGwvNS

Exercise 8 Using our notation conventions from the textbook, which one of the following kinds of things is $u$ ?

A constant       A function name       An input name      

question id: 3Yxhvu

Exercise 9 Can function names be multiple letters, e.g. g3() or altitude()?

Yes       No      

question id: jRqRwj

Exercise 10 A formal input name is the name used to identify an input in the definition of a function.

In MOSAIC Calculus, will formal input names have subscripts, like $x_0$ or $u_2$?

Yes       No      

question id: qx5fhu

Exercise 11 In the book, what is meant by the word “variable”?

input to a function

output from a function

A column in a data table.

All of the above.

question id: UyVrjr

Exercise 12 What is the name of the function being defined in $a(b)\equiv 3x+2b$?

a       b       x      

question id: jL2bMb

Exercise 13 What is the name of the input to the function being defined in $a(b)\equiv 3x+2b$?

a       b       x      

question id: 7EiMPI

Exercise 14 What is wrong with this function definition? $$\text{dorothy(kansas)}\equiv niec{e}_{o}f(AuntieEm)\times \text{kansas}?$$

You cannot name a function “dorothy.”

“kansas” is a US state, not the name of an argument.

“dorothy” and “kansas” should be capitalized.

Auntie Em is a person, not a number.

Nothing.

question id: 2XfUTb

Exercise 15 What’s wrong with this function definition? $$\text{electric}(z)\equiv 3z+\ln ()$$

No input has been given to $\ln ()$.

‘electric()’ should have been written as E().

Nothing

question id: 7z5PpG

Exercise 16 You are modeling the population of E. coli growing in optimal conditions. (Optimal for the E. coli, not for you!) In R, you’ve written population <- makeFun(100*exp(hours) ~ hours) What’s the correct definition in traditional notation?

$\text{population}\equiv 100e^{\text{hours}}$

$\text{population}(t)\equiv 100e^{\text{hours}}$

$\text{population}(\text{hours})\equiv 100e^{\text{hours}}$

None of the above.

question id: PN4DcB

Exercise 17 In traditional notation, $$\text{Celsius}(\text{Fahrenheit})\equiv \frac{5}{9}(\text{Fahrenheit}-32)$$ defines a function named Celsius(). This of the following correctly defines that function in R?

Celsius(Fahrenheit) <- makeFun(5*(Fahrenheit-32)/9)

Celsius <- makeFun(5/9*Fahrenheit - 32 ~ Fahrenheit)

Celsius() <- makeFun(5*(Fahrenheit-32)/9 ~ Fahrenheit)

Celsius <- makeFun(5*(Fahrenheit-32)/9 ~ Fahrenheit)

Celsius(Fahrenheit) <- makeFun(5*(Fahrenheit-32)/9 ~ Fahrenheit)

question id: aBQhv1

Exercise 18 Which of these roles does the symbol $y_0$ suggest using the MOSIAC Calculus conventions for notation?

a constant

an input to a function

the output from a function

a function name

it is nonsense

question id: z4rS9z

Exercise 19 Given the definition $g(z)\equiv z\sin (z)$, which of these does the symbol $z$ suggest using our CalcZ notation conventions?

a constant

the input to the function

the output from the function

the function name

it is nonsense

question id: KJMU3m

Exercise 20 Given the definition $g(z)\equiv z\sin (z)$, which of these does the symbol $g$ suggest using our CalcZ notation conventions?

a constant

the input to the function

the output from the function

the function name

it is nonsense

question id: Tel7VL

Exercise 21 Given the definition $\text{pressure}(H)\equiv \exp (-H/10)$, which of these does the symbol $H$ suggest using our CalcZ notation conventions?

a constant

the input to the function

the output from the function

the function name

it is nonsense

question id: 7HDk69

Exercise 22 Given the definition $\text{pressure}(H)\equiv \exp (-H/10)$, which of these does the symbol pressure suggest using our CalcZ notation conventions?

a constant

the input to the function

the output from the function

the function name

it is nonsense

question id: MGAKqk

Exercise 23 In the definition $h(z)\equiv az+b$ what is the symbol $z$?

a constant

the input to the function

the output from the function

the function name

it is nonsense

question id: JcuC9H

Exercise 24 In the definition $h(z)\equiv az+b$ what is the symbol $a$?

a constant

the input to the function

the output from the function

the function name

it is nonsense

question id: BsvFUW

Exercise 25 Can function names have subscripts or superscripts, like $g_0()$ or $f^{\prime }()?$

Yes       No      

question id: jsH1Hk

Exercise 26 What is the name of the function being defined in $a(b)\equiv 3x+2b$?

a       b       x      

question id: fname1

Exercise 27 What is the name of the input to the function being defined in $a(b)\equiv 3x+2b$?

a       b       x      

question id: fname2

Exercise 28 What is wrong with this function definition? $$\text{text{dorothy(kansas)} equiv text{niece\_of(Auntie\_Em)} times text{kansas}}$$

You can’t name a function “dorothy.”       “kansas” is a US state, not the name of an argument.       “dorothy” and “kansas” should be capitalized.       Auntie Em is a person, not a number.       Nothing.      

question id: fname3

Exercise 29 What’s wrong with this function definition? $$\text{electric}(z)\equiv 3z+\ln ()$$

No input has been given to $\ln ()$.       “electric()” should have been written as E().       Nothing      

question id: fname4

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