FUNCTIONS
Tanreet

Domain - Independent Variable (all "x" values)

Range - Dependent Variable (all "y" values")

Format for stating the domain and range

Set Notation: a way of writing a set of items or numbers

ex. {XER-X cannot=0}

Examples

By looking at the graph you can see all x values are less than 3 and you can see all y values are greater than 0

By looking at the graph you can see all x values are greater than -5 and you can see all y values are great than o

What is a inverse function ?

two functions that “reverse” each other

"x" and "y" are switched

The inverse of f (x), is denoted as f^-1(x)

read as “f inverse at x”

How do find inverse of a function?

Translations

Vertical Translations

if the function is y= f(x) + c, function shifts up
if the function is y= f(x) - c, function shifts down

Horizontal Translations

if the function is y = f(x-d) function shifts right
if the function is y = f(x+d) function shifts left

Reflections

if a < 0 - reflection in the x-axis

if k < 0 - reflection in the y-axis

Vertical and Horizontal Stretches & Compressions

if a > 1 - vertical stretch

if a < 1 - vertical compression

if k > 1 - horizontal compression

if k < 1 - horizontal stretch

Use this knowledge to graph functions

purple has gone through transformations

purple has gone through transformations

Domain - Independent Variable (all "x" values)

Range - Dependent Variable (all "y" values")

Set Notation: a way of writing a set of items or numbers

ex. {XER-X cannot=0}

Relations vs Functions

Relation: is a set of ordered pairs (x,y)

Function: A special relation. An ordered pair where for every value of x, there is only one value of y.

Function or Not

Vertical Line Test: If any vertical line passes through more than one point on the graph of a relation then the relation is NOT a function

passes vertical line test

does not pass vertical line test

Check X Values: If there are 2 or more x-values for a single y-value, then the graph is not a function

Lines: Always a function with the exception of vertical lines Circle: Never a function
Parabola: Always a function

f(x) is used to represent the value of the dependant variable also known as the output

Read as “f at x” or “f of x”

f(x)=y; gives you a (x,y) pairing

Other symbols can be used to name the outputs of functions instead of “f” to fit problem

Solve?

Given: X
Find: f(x)

Given: f(x)
Find: X

The simplest, or base function in a family

Parent Functions
Linear Function
Quadratic Function
Square Root Function
Absolute Value Function
Reciprocal Function

Asymptote: A line that the graph of a relation or function gets close to, but never touches