FUNCTIONS Tanreet

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FUNCTIONS Tanreet

Parent Graphs (2.3)

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

Reciprocal

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

Absolute Value

Square Root

Quadratic

Linear

The simplest, or base function in a family

Function Notation (2.2)

Solve?

Given: f(x) Find: X

solve for x

Given: X Find: f(x)

solve for y

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

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”

Relations & Functions (2.1)

Function or Not

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

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

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

not a function

does not pass vertical line test

function

passes vertical line test

Relations vs Functions

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

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

Using Transformations to Graph Functions

Use this knowledge to graph functions

Vertical and Horizontal Stretches & Compressions

if k < 1 - horizontal stretch

if k > 1 - horizontal compression

if a < 1 - vertical compression

if a > 1 - vertical stretch

Reflections

if k < 0 - reflection in the y-axis

if a < 0 - reflection in the x-axis

Translations

Horizontal Translations

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

Vertical Translations

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

Inverse of a Function (2.5)

How do find inverse of a function?

switching x & y and isolating for y

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

read as “f inverse at x”

What is a inverse function ?

two functions that “reverse” each other

"x" and "y" are switched

Domain & Range (2.4)

Examples

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

states domain and range

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

Format for stating the domain and range

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

ex. {XER-X cannot=0}

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

Domain - Independent Variable (all "x" values)