# Study sets matching "college algebra functions"

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

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

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…

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

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 = __

Cubic

Absolute Value

Logarithmic

Logistic

volume of a box Domain: height Range: volume

bouncing cart on flat track Domain: time Range: distance

Measuring Earthquakes Domain:energy Range: power

Radioactive Decay Domain: time Range: amount

Cubic

volume of a box Domain: height Range: volume

Absolute Value

bouncing cart on flat track Domain: time Range: distance

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

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…

complex number

real number

rational number

irrational number

a number of the form a + bi where a and b are real numbers. Co…

numbers that are either rational or irrational. A real number…

a number that can be expressed as a/b, the ratio of two intege…

a number that cannot be expressed as a/b, the ratio of two int…

complex number

a number of the form a + bi where a and b are real numbers. Co…

real number

numbers that are either rational or irrational. A real number…

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,🔀)

x-intercepts

y-intercepts

Vertical Asymptotes

Horizontal Asymptotes

roots of the numerator but NOT the denominator

plug 0 in for all the parts of the function

Roots of the denominator but NOT the numerator. If it is a roo…

If the degree of the numerator is less than that of the denomi…

x-intercepts

roots of the numerator but NOT the denominator

y-intercepts

plug 0 in for all the parts of the function

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…

complex number

real number

rational number

irrational number

a number of the form a + bi where a and b are real numbers. Co…

numbers that are either rational or irrational. A real number…

a number that can be expressed as a/b, the ratio of two intege…

a number that cannot be expressed as a/b, the ratio of two int…

complex number

a number of the form a + bi where a and b are real numbers. Co…

real number

numbers that are either rational or irrational. A real number…

complex number

real number

rational number

irrational number

a number of the form a + bi where a and b are real numbers. Co…

numbers that are either rational or irrational. A real number…

a number that can be expressed as a/b, the ratio of two intege…

a number that cannot be expressed as a/b, the ratio of two int…

complex number

a number of the form a + bi where a and b are real numbers. Co…

real number

numbers that are either rational or irrational. A real number…

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