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What is the average Rate of Change for…

Which direction does f(x)=+c move in s…

What direction does f(x)-c move in sta…

Which direction does f(x+c) move

f(x2)-f(x1) / x2-x1

Up

Down

Left

What is the average Rate of Change for…

f(x2)-f(x1) / x2-x1

Which direction does f(x)=+c move in s…

Up

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…

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

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 tabl…

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…

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

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…

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 variabl…

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

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

Relation

Any set of ordered pairs

Domain

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

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

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) ti…

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

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

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) ti…

Domains for functions

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

Function

Function Notation

Function Generic Venn Diagram

Satisfy the Rule

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

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

Function

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

Function Notation

complex number

real number

rational number

irrational number

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

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

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

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

complex number

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

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. C…

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

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

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

complex number

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

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,🔀)

When we can perform the operations of…

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…

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

Solving quadratic equations--

Ax+By=C

When we can perform the operations of…

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

What is a function?

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

complex number

real number

rational number

irrational number

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

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

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

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

complex number

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

real number

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

Absolute value

Algebraic expression

Arithmetic expression

A systyem of equations

The distance from 0 to n on the number line |n|= n when n>=0…

An expression containing numbers, operation signs, and variab…

An expression containing numbers and operation signs, such as…

Two or more equations considered together.

Absolute value

The distance from 0 to n on the number line |n|= n when n>=0…

Algebraic expression

An expression containing numbers, operation signs, and variab…

complex number

real number

rational number

irrational number

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

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

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

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

complex number

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

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. C…

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

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

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

complex number

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

real number

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

Quadratic Equation

Zero-Product Property

Completing the Square

Quadratic Formula

The equation of form:... ax + bx + c = 0... where a , b , and c are…

AB = 0 if and only if A = 0 or B = 0

x^2 + bx + (b/2)^2 = (x +/2)^2

The roots of the quadratic equation ax^2 + bx + + c = 0 where…

Quadratic Equation

The equation of form:... ax + bx + c = 0... where a , b , and c are…

Zero-Product Property

AB = 0 if and only if A = 0 or B = 0

complex number

real number

rational number

irrational number

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

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

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

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

complex number

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

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. C…

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

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

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

complex number

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

real number

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

Variable

Expression

Equation

Algebraic

A letter which represents or stands for in a value

A combination of variables, numbers and operators

Two expressions joined by an equal sign

An expression that does not contain words

Variable

A letter which represents or stands for in a value

Expression

A combination of variables, numbers and operators

5√2

(13/2 , -45/2)

(17,-10)

(16,-11)

Find the distance between the points (4,-25) and (9,-20)

Find the midpoint of (4,-25) and (9,-20)

Find the other endpoint given the midpoint (12,-8) and endpoi…

Find the other endpoint given the midpoint (12,-15) and endpo…

5√2

Find the distance between the points (4,-25) and (9,-20)

(13/2 , -45/2)

Find the midpoint of (4,-25) and (9,-20)

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 se…

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

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 se…

Counting Numbers

Whole Numbers

Integers

Rational Numbers

The numbers used to count; the members of the set (1,2,3,4,5,…

Natural numbers ( counting numbers) and zero; 0, 1, 2, 3...

All whole numbers (both positive and negative) and zero

All positive and negative integers, fractions and decimal num…

Counting Numbers

The numbers used to count; the members of the set (1,2,3,4,5,…

Whole Numbers

Natural numbers ( counting numbers) and zero; 0, 1, 2, 3...

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 a…

the product of three numbers may be grouped differently witho…

in exponential notation, the expression that is being multipl…

Algebraic expression

constants and variables combined using addition, subtraction,…

Associative property of addition

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

Correlation coefficient

Decreasing linear function

Extrapolation

Horizontal line

a value, r, between -1 and 1 that indicates the degree of lin…

a function with a negative slope: If f (x) = mx + b, then m <…

predicting a value outside the domain and range of the data

a line defined by f (x) = b, where b is a real number. The sl…

Correlation coefficient

a value, r, between -1 and 1 that indicates the degree of lin…

Decreasing linear function

a function with a negative slope: If f (x) = mx + b, then m <…

complex number

real number

rational number

irrational number

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

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

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

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

complex number

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

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. C…

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

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

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

complex number

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

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. C…

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

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

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

complex number

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

real number

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