2 Functions of One Variable

Question 1

When is a function monotonic?

Answer 1

When it is increasing or decreasing over a set domain

Question 2

When is a function strictly increasing?

Answer 2

When x1

Question 3

What is the format of a power function

Answer 3

Y=Ax^r

Where r and A are constants

Question 4

What are examples of economic applications of power functions?

Answer 4

Production function y=x^r (0

Question 5

What is the format of an exponential function

Answer 5

Y=Ab^x

Where A and b are constants

Question 6

What is the inverse of y=ln(x)

Answer 6

Y=e^x
X=e^y ??

Question 7

How are y=ln(x) and y=e^x graphically related?

Answer 7

They are symmetrical in the line y=x

Question 8

What is a^(loga(x)) equal to?

Answer 8

X

Question 9

How else can log(xy) be written?

Answer 9

Log(x) + log(y)

Question 10

How else can log(x) + log(y) be written

Answer 10

Log(xy)

Question 11

How else can log(x/y) be written?

Answer 11

Log(x)-log(y)

Question 12

How else can log(x)-log(y) be written

Answer 12

Log(x/y)

Question 13

How else can log(x^p) be written

Answer 13

Plog(x)

Question 14

How else can plog(x) be written

Answer 14

Log(x^p)

Question 15

What is loga(a) equal to?

Answer 15

1

Question 16

How else can loga(x)/loga(b) be written?

Answer 16

Logb(x)

Question 17

Describe the graphical change that occurs when t(t) is created by adding f(t) and m(t)

Answer 17

t(t) is the vertical sum of m(t) and f(t)

Question 18

If F(x)=f(x) x g(x) what is F(x) called?

Answer 18

The product of f and g

Question 19

If F(x)=f(x)/g(x) what is F(x) called?

Answer 19

The quotient of f and g

Question 20

What is a composite function?

Answer 20

When two functions are combined to create a composite function

E.g h(x)= f(g(x))

Question 21

When does an inverse function exist?

Answer 21

If the original function is strictly monotonic. ie the function is one to one

Question 22

Domain

Answer 22

Set on which a function is defined

Question 23

Codomain

Answer 23

Set on which output of f(x) is constrained to fall

Question 24

Range

Answer 24

Set of elements of Y associated with elements of X

Question 25

What is a continuous function?

Answer 25

One which can be drawn without lifting the pen from the paper ie no jumps