3. Functions Flashcards
What is a function like
A number machne
Input of function
Domain (x)
Domain (x)
An input of function
Output of function
Range (y)
Range (y)
Output of function
How are functions written
f (x)
Given g (x) = 3x^2 - x, find the value of g (x-2)
3x2 - 13x + 14
Method for solving basic function
- Write our function
- Sub domain into function
- Simplify
If h(x) = x / (2x +3), simplify h (1/x)
1 / 2 + 3x
Two restrictions on domain
You can’t take the square root of a -ve
You can’t divide by 0
What does a restriction on the domain mean
Function will be undefined for a certain value of x
Find for
Find for what value (s) of x is f(x) undefined and state a suitable domain
for (x) = /(x-3)
x is undefined when x - 3 < 0, x < 3
domain = x greater than or equal to 3
Find for what value (s) of x is f(x) undefined and state a suitable domain
f(x) = 1 / x(x+5)
x ≠ 0, -5
Set
Collection of items with a common property
Collection of items with a common property
Set
Element/member
An item in a set
An item in a set
Element/member
N set
Natural numbers
Natural numbers
N
W set
Whole numbers
Whole numbers
W set
Z set
Integers
Integers
Z set
Q set
Rational numbers
Rational numbers
Q set
R set
Real numbers
Real numbers
R set
Order of sets
N
W
Z
Q
R
Order of sets
N
W
Z
Q
R
E =
Belongs to
Empty set
No elements in a set
No elements in a set
Empty set
3 ways functions can be written
Equations, arrow diagrams, graphs
What must you ensure when writing a function as a arrow diagram
Each domain only links to one member of the range
Displaying function as graph
Domain is x coordinate
Range is y coordinate
Composite function
Function that combines more than one function
Function that combines more than one function
Composite function
Method for solving composite functions
- Find internal function by subbing x into bracketed equation
- Solve equation
- Sub answer into outer function
- Solve equation
If f(x) = 3x + 7 and g(x) = 5x, find f (g(x)) when x is 7
112
Given f(x) = 2x + 3, what is h(x) if h (x) = f (x / (x+1))
5x + 3 / x + 1
Inverse function
Each element in B links to one element in A
Each element in B links to one element in A
Inverse function
Of the original function multiplies by 5, what is the inverse
Divided by 5
Method of finding inverse function from original function
- Change f(x) to y
- Change subject of formula to x
- Swap x for f-1 and swap y for x
Find the inverse of f(x) = 4x + 3
f-1 (x) = x - 3 / 4
Find the inverse of f(x) = 4x + 3
f-1 (x) = x - 3 / 4
Order of operations in finding inverse functions
Opposite of bodmas
Find the inverse of f(x) = 1/3 (x+7)
f-1(x) = 3x - 7
Find f(f-1(x)) if f(x) = 5x + 2
x
applying a function to its inverse or vice versus gives…
x
How can the graph of an inverse function be found
By reflecting the graph of f(x) in the line y=x
By reflecting the graph of f(x) in the line y=x
Find graph of inverse
Coords of inverse in relation to function
The x and y coordinates switch
Exponential function form
f(x) = a^x
or
y = a^x
f(x) = a^x
or
y = a^x
Exponential
Anything to the power of 0 =
1
What points does an exponential pass through
(0, 1) and (1, a)
what graph passes through (0, 1) and (1, a)
Exponential
Direction of exponential graph if a > 1
Up from left to right
Direction of exponential graph if 0 < a < 1
Down from left to right
Form of log function
y = logax
y = logax
Logarithmic graph
Log graphs are the inverse of what
Exponential functions
Inverse of exponential functions
Logarithmic functions
What points do a log graph pass through
(1, 0) and (a, 1)
What always passes through (1, 0) and (a, 1)
Logarithmic graph
