3. Functions

Question 1

What is a function like

Answer 1

A number machne

Question 2

Input of function

Answer 2

Domain (x)

Question 3

Domain (x)

Answer 3

An input of function

Question 4

Output of function

Answer 4

Range (y)

Question 5

Range (y)

Answer 5

Output of function

Question 6

How are functions written

Answer 6

f (x)

Question 7

Given g (x) = 3x^2 - x, find the value of g (x-2)

Answer 7

3x2 - 13x + 14

Question 8

Method for solving basic function

Answer 8

1. Write our function
2. Sub domain into function
3. Simplify

Question 9

If h(x) = x / (2x +3), simplify h (1/x)

Answer 9

1 / 2 + 3x

Question 10

Two restrictions on domain

Answer 10

You can’t take the square root of a -ve

You can’t divide by 0

Question 11

What does a restriction on the domain mean

Answer 11

Function will be undefined for a certain value of x

Question 12

Find for

Question 13

Find for what value (s) of x is f(x) undefined and state a suitable domain

for (x) = /(x-3)

Answer 13

x is undefined when x - 3 < 0, x < 3

domain = x greater than or equal to 3

Question 14

Find for what value (s) of x is f(x) undefined and state a suitable domain

f(x) = 1 / x(x+5)

Answer 14

x ≠ 0, -5

Question 15

Set

Answer 15

Collection of items with a common property

Question 16

Collection of items with a common property

Answer 16

Set

Question 17

Element/member

Answer 17

An item in a set

Question 18

An item in a set

Answer 18

Element/member

Question 19

N set

Answer 19

Natural numbers

Question 20

Natural numbers

Answer 20

N

Question 21

W set

Answer 21

Whole numbers

Question 22

Whole numbers

Answer 22

W set

Question 23

Z set

Answer 23

Integers

Question 24

Integers

Answer 24

Z set

Question 25

Q set

Answer 25

Rational numbers

Question 26

Rational numbers

Answer 26

Q set

Question 27

R set

Answer 27

Real numbers

Question 28

Real numbers

Answer 28

R set

Question 29

Order of sets

Answer 29

N W Z Q R

Question 30

Order of sets

Answer 30

N W Z Q R

Question 31

E =

Answer 31

Belongs to

Question 32

Empty set

Answer 32

No elements in a set

Question 33

No elements in a set

Answer 33

Empty set

Question 34

3 ways functions can be written

Answer 34

Equations, arrow diagrams, graphs

Question 35

What must you ensure when writing a function as a arrow diagram

Answer 35

Each domain only links to one member of the range

Question 36

Displaying function as graph

Answer 36

Domain is x coordinate Range is y coordinate

Question 37

Composite function

Answer 37

Function that combines more than one function

Question 38

Function that combines more than one function

Answer 38

Composite function

Question 39

Method for solving composite functions

Answer 39

1. Find internal function by subbing x into bracketed equation 2. Solve equation 3. Sub answer into outer function 4. Solve equation

Question 40

If f(x) = 3x + 7 and g(x) = 5x, find f (g(x)) when x is 7

Answer 40

112

Question 41

Given f(x) = 2x + 3, what is h(x) if h (x) = f (x / (x+1))

Answer 41

5x + 3 / x + 1

Question 42

Inverse function

Answer 42

Each element in B links to one element in A

Question 43

Each element in B links to one element in A

Answer 43

Inverse function

Question 44

Of the original function multiplies by 5, what is the inverse

Answer 44

Divided by 5

Question 45

Method of finding inverse function from original function

Answer 45

1. Change f(x) to y 2. Change subject of formula to x 3. Swap x for f-1 and swap y for x

Question 46

Find the inverse of f(x) = 4x + 3

Answer 46

f-1 (x) = x - 3 / 4

Question 47

Find the inverse of f(x) = 4x + 3

Answer 47

f-1 (x) = x - 3 / 4

Question 48

Order of operations in finding inverse functions

Answer 48

Opposite of bodmas

Question 49

Find the inverse of f(x) = 1/3 (x+7)

Answer 49

f-1(x) = 3x - 7

Question 50

Find f(f-1(x)) if f(x) = 5x + 2

Answer 50

x

Question 51

applying a function to its inverse or vice versus gives…

Answer 51

x

Question 52

How can the graph of an inverse function be found

Answer 52

By reflecting the graph of f(x) in the line y=x

Question 53

By reflecting the graph of f(x) in the line y=x

Answer 53

Find graph of inverse

Question 54

Coords of inverse in relation to function

Answer 54

The x and y coordinates switch

Question 55

Exponential function form

Answer 55

f(x) = a^x or y = a^x

Question 56

f(x) = a^x or y = a^x

Answer 56

Exponential

Question 57

Anything to the power of 0 =

Answer 57

1

Question 58

What points does an exponential pass through

Answer 58

(0, 1) and (1, a)

Question 59

what graph passes through (0, 1) and (1, a)

Answer 59

Exponential

Question 60

Direction of exponential graph if a > 1

Answer 60

Up from left to right

Question 61

Direction of exponential graph if 0 < a < 1

Answer 61

Down from left to right

Question 62

Form of log function

Answer 62

y = logax

Question 63

y = logax

Answer 63

Logarithmic graph

Question 64

Log graphs are the inverse of what

Answer 64

Exponential functions

Question 65

Inverse of exponential functions

Answer 65

Logarithmic functions

Question 66

What points do a log graph pass through

Answer 66

(1, 0) and (a, 1)

Question 67

What always passes through (1, 0) and (a, 1)

Answer 67

Logarithmic graph