# Study sets matching "college algebra functions"

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Constant Function... F(x)=c

Identity Function... F(x)=x

Squaring Function... F(x)=x^2

Cubing Function... F(x)=x^3

D:(-OO,OO)... R:{c}... Increases: (-OO,OO)... Even

D:(-OO,OO)... R:(-OO,OO)... Increases: (-OO,OO)... Odd

D:(-OO,OO)... R:[0,OO)... Increases:(0,OO)... Decreases:(-OO,0)... Odd

D:(-OO,OO)... R:(-OO,OO)... Increases:(-OO,OO)... Odd

Constant Function... F(x)=c

D:(-OO,OO)... R:{c}... Increases: (-OO,OO)... Even

Identity Function... F(x)=x

D:(-OO,OO)... R:(-OO,OO)... Increases: (-OO,OO)... Odd

relation

domain

range

the 5 ways to write a relation

any set of ordered pairs

x-values, independent variables, input

y-values, dependent variables, output

1.) set of ordered pairs: {(1,2), (3,4), (5,6)}... 2.) as a table…

relation

any set of ordered pairs

domain

x-values, independent variables, input

linear function

constant function

identity function

square function

f(x) = mx+b, m and b are real numbers

f(x) = b, b is a real number... even function

f(x) = x... odd function... anchor point is (0,0)... right 1 - up 1... r…

f(x) = x^2... even function... anchor point is (0,0)... left or right…

linear function

f(x) = mx+b, m and b are real numbers

constant function

f(x) = b, b is a real number... even function

Linear Graph

Linear because X is to the first power

Linear Table

Absolute Value Graph

Graph is a straight line

F(X)=4x-3

The function increases or decreases by a constant rate of chan…

Graph is a V shape

Linear Graph

Graph is a straight line

Linear because X is to the first power

F(X)=4x-3

How do you find the domain if the squar…

How do you find the domain if X is on t…

How do find the domain when the square…

How do you find the zeros if there's ju…

Set it greater to or equal to 0. ( x+5_> 0 )

Set both not equal to 0. X-2=/0 and X+2=/0

Set it greater than zero. x+5>0

Factor. (How many x's can you take away from each)

How do you find the domain if the squar…

Set it greater to or equal to 0. ( x+5_> 0 )

How do you find the domain if X is on t…

Set both not equal to 0. X-2=/0 and X+2=/0

Linear ... F(x)= x

Quadratic ... F(x)= x^2

Cubic... F(x)= x^3

Rational inverse... F(x)= 1/x

Domain: (-🔀,🔀)... Range: (-🔀,🔀)

Domain: (-🔀,🔀)... Range: [0,🔀)

Domain: (-🔀,🔀)... Range: (-🔀,🔀)

Domain: (-🔀,0)U(0,🔀)... Range: (-🔀,0)U(0,🔀)

Linear ... F(x)= x

Domain: (-🔀,🔀)... Range: (-🔀,🔀)

Quadratic ... F(x)= x^2

Domain: (-🔀,🔀)... Range: [0,🔀)

Horizontal Asymptotes.....

1st Rule...

2nd Rule...

3rd Rule...

rules

if the degree (N) < degree (D) then the horizontal asymptote i…

if the degree (N) = degree (D) then the horizontal asymptote y…

if degree(N) > degree (D) then there is no horizontal asymptote

Horizontal Asymptotes.....

rules

1st Rule...

if the degree (N) < degree (D) then the horizontal asymptote i…

Relation

Domain

Range

The 5 ways to write a relation

Any set of ordered pairs

The set of all first components... (X value, independent variable…

The set of all second components ... (Y value, dependent variable…

☆Set of ordered pairs ... {(1/2,3), (2,-3), (4,7), (1,2/3)}... ☆Tabl…

Relation

Any set of ordered pairs

Domain

The set of all first components... (X value, independent variable…

Asymptote

Vertical Asymptote

Horizontal Asymptote

X Intercepts

A line that the function approaches but never touches

Where X will cause 0 in the factored denominator... X = __

If the degree on top is higher = no HA... If the degrees are equa…

Replace Y with 0 and solve for X... Make sure its the X values on…

Asymptote

A line that the function approaches but never touches

Vertical Asymptote

Where X will cause 0 in the factored denominator... X = __

Slope of line

Equation of line: slope-intercept form

Equation of line: point-slope form

Equation of line: intercept form

Give two points (x1, y1) and (x2, y2), m = rise/run

y = mx + b, where m is the slope, b is the y-intercept

Give two points (x1, y1) and (x2, y2), ... (y - y1) = m(x - x1),…

"Given x-intercept a and x/a = y/b = 1 y-intercept b,

Slope of line

Give two points (x1, y1) and (x2, y2), m = rise/run

Equation of line: slope-intercept form

y = mx + b, where m is the slope, b is the y-intercept

When we can perform the operations of a…

What is a function?

The quadratic formula

Standard Form of a Linear Equation

If two (or more) functions have the same domain, then we can p…

Function is a relation where one components (x) corresponds on…

Solving quadratic equations--

Ax+By=C

When we can perform the operations of a…

If two (or more) functions have the same domain, then we can p…

What is a function?

Function is a relation where one components (x) corresponds on…

An equation is a function if...

Definition of a function

Vertical Line Test

Even Function

each x-value has only one y-value

a correspondence from a first set, called the domain, to a sec…

if any vertical line intersects a graph in more than one point…

f(-x) = f(x), reflected over y-axis

An equation is a function if...

each x-value has only one y-value

Definition of a function

a correspondence from a first set, called the domain, to a sec…

Function

Function Notation

Function Generic Venn Diagram

Satisfy the Rule

A *function* consists of three things: ... 1) A set called the D…

The coordinates of a point (a, b) are said to *satisfy the rul…

Function

A *function* consists of three things: ... 1) A set called the D…

Function Notation

Algebraic expression

Associative property of addition

Associative property of multiplication

Base

constants and variables combined using addition, subtraction,…

the sum of three numbers may be grouped differently without af…

the product of three numbers may be grouped differently withou…

in exponential notation, the expression that is being multipli…

Algebraic expression

constants and variables combined using addition, subtraction,…

Associative property of addition

the sum of three numbers may be grouped differently without af…

operation on functions

Domains for functions

Domain example for (f+g)(x), (f-g)(x),…

Domain example for (f÷g)(x)

(f+g)(x) = f(x)+ g(x)... (f-g)(x) = f(x)- g(x)... (fg)(x) = f(x) tim…

For sum, difference, and product of f and g share the same dom…

for f(x) = 2 + √(x-1) and g(x)= x² - 4... When x≥1, then f(x) = 2…

for f(x) = 2 + √(x-1) and g(x)= x² - 4... It would look like ( 2…

operation on functions

(f+g)(x) = f(x)+ g(x)... (f-g)(x) = f(x)- g(x)... (fg)(x) = f(x) tim…

Domains for functions

For sum, difference, and product of f and g share the same dom…