Khan Academy Algebra

example of an open interval

(-2,3) or x is greater than negative 2 and is less than 3

what is the slope of a horizontal line?

0

example of sequence

1,3,5,7,9 difference: +2

tangent line

A line that intersects a curve once and only once

relative maximum

A point on the graph of a function where no other nearby points have a greater y-coordinate.

relative minimum

A point on the graph of a function where no other nearby points have a lesser y-coordinate.

negative function

A portion of a function where the y-values are less than 0 for all x-values

what is a unit rate

A rate with a denominator of 1.

arithmetic sequence

A sequence in which the difference between any two consecutive terms is the same.

example of a relationship in a function

A tree grows 20 centimeters per year. so the height is related to its age using the function h. h(y)=20y

what is an equation

An Equation is a statement that two mathematical expressions are equal.

closed interval

An interval that includes both of its ending points and all the points between these ending points

standard form

Ax+By=C where A, B, and C are real numbers and A & B are not both zero.

complex number symbol

C

Equation vs Expression

Equation relation sign (=or >) you solve is a sentence DO SAME TO BOTH SIDES of the equal sign (for these allowable operations: + − × ÷ √ ( )ⁿ add, subtract, multiply, divide, "take a root" and "raise to a power") Expression no relation size you simplify (not solve) ... can multiply by 1 or combine like terms and factor is a phrase

Imaginary number symbol

I

example of independent and dependent variables

John works x hours and makes $3 per hour. what is his total in y after x hours? 3x=y the dependent is total because it depends on how many hours worked the independent is y because it is the variable being manipulated

natural numbers symbol

N

rational numbers symbol

Q

Real numbers symbol

R

what is function notation?

Replacing the y with f(x) Example: y = 2x + 3 to f(x) = 2x + 3

what is a function?

System-defined formula

Double inequality

Two inequalities can often be combined into a DOUBLE INEQUALITY or COMPOUND INEQUALITY to indicate that the numbers lie between two fixed values. e.g. -16<3x+5<20

compound inequality

Two or more inequalities joined together by "and" or "or"

what is the slope of a vertical line?

Undefined, because we can't divide by 0.

integers symbol

Z

example of an opened and closed interval

[-2,3) or x is greater than or equal to negative 2 and is less than 3

example of a closed interval

[-2,3] or x is greater than or equal to -2 and x is less than or equal to 3

set builder notation

a concise way of writing a solution set

positive function

a portion of a function where the y-values are greater than 0 for all x-values

geometric sequence

a sequence in which each term is found by multiplying the previous term by the same number

recursive formula of arithmetic sequence

a(n)= a(n-1)+difference a= output n= nth term

explicit formula of arithmetic sequence

a(n)=a1+d(n-1) n= nth term a=function a in terms of term n

example of variable

a+1=x a and x are variables

arithmetic sequences can use only what two operations?

addition or subtraction

what is a linear equation?

algebraic expression where the highest power is 0 i.e. 2x+2

what is an interval

all numbers between two numbers

domain of sequence

all possible inputs of function since domain is in terms of nth term its always positive

algebraic equation

an expression with one or more variables i.e. 2x+1=5

open interval

an interval that does not include its endpoints

what is an open and closed interval?

an interval where one endpoint is included and the other is not

what is an algebraic expression

an set of terms that represent a value but no equal sign

what do compound inequalities joined by "and" mean

both inequalities must be satisfied for the solution to be considered true

why is standard form useful?

can be used to find intercepts of a line by setting x or y equal to zero

slope of a line

change in y over change in x. a.k.a rise over run

what can you do to terms with the same variable in an equation?

combine them i.e. 2x+3y-2x 1x+3y

common difference of an arithmetic sequence

constant difference between consecutive terms

how do you set up unit rate?

dependent variable/independent variable i.e. distance per hour depends on speed 45m/hr i.e. 45m/1hr

what should you do to parenthesis before combining like terms

distribute the parenthesis properly i.e 2x(3x+25)-2x 6x^2+48x

inverse of multiplication

division a(1/a)=1

how do you get rid of a variable on one side of the equation?

do the opposite operation on both sides that cancels it out on the desired side

what do compound inequalities joined by "or" mean

either of the inequalities can be true to considered true

what is a true equation?

expression on both sides of equal sign are equal

what is an equivalent expression?

expressions that represent the same value i.e. 4a+8=2(2a+4)

example of interval domain

f(x)=3/x x= any real value except zero (3/0= undefined) (-infinity,0) U (0, infinity)

common example of functions

f(x)=x^2 where x is the input, f(x) is the output, ^2 is the relationship

plotting greater than or equal to or less than or equal to on number line

filled in circle + line

when multiplying or dividing inequalities by a negative what happens to the inequality sign?

flip it i.e. -2x>4 x<-2

interval of domain

formal way of describing continuous set of real values that can describe a domain

absolute maximum of a function

highest value of a function written as (x,y)

what is the relationship of a function?

how the input relates to the output

when does an algebraic equation have only one solution?

if there is one number equaling a variable i.e. x=5

visualize a function

input, function, output

what are the three parts of a function?

input, relationship, output

absolute minimum of a function

lowest value of a function

what is the input of a function?

number that is inserted into the function f(X)=a

plotting greater than or less than on number line

open circle + line

common ratio of geometric sequence

ratio between consecutive terms represented as a multiplier

how does a function work?

relates an input to an output

What is a a way to represent an interval in a fancy way

set builder notation

What is the "domain" of a function?

set of all inputs in which the function has a defined output

Sum of Consecutive odd or even Integers

set up as x, x+2, x+4 ( represents relations ship between x and next odd or even integer e.g 1,3,5)

inverse of addition

subtraction a+(-a)=0

what is a variable

symbol for an unknown value

what does the slope-intercept form represent

the equation of a line

secant line

the line through two points on a curve

what is the output of a function?

the result of the input

what is the range of a function?

the set of all possible outputs

What is the function name of a function

the variable before the parentheses i.e. F(x)

what is the argument of a function?

the variable inside the parentheses of a function i.e. f(X)

x-intercept

the x-coordinate of a point where a graph crosses the x-axis

Y-intercept

the y-coordinate of a point where a graph crosses the y-axis

what must be true of the input values of a function

they can only represent one value of the output.

what happens when you divide by 0?

undefined

average rate of change of a curve

use coordinates of secant line to find average rate of change over an interval

what is an independent variable?

variable that is manipulated

what is a dependent variable?

variable that is measured

when does an equation have infinite solutions?

when both sides of the equation have equal numerical values i.e. 13=13

when does an equation have zero solutions

when there are two different values on each side of the equal sign i.e. 4=6 (not true)

decreasing function interval

when y<0

increasing function interval

when y>0

the independent variable is usually on what axis?

x-axis

equation for a vertical line

x=a

what is point-slope form?

y minus y1 equals m times x minus x1

The dependent variable is usually on what axis?

y-axis

point-slope form

y-y1=m(x-x1)

slope formula given two points

y2-y1/x2-x1

equation for a horizontal line

y=b

slope intercept form

y=mx+b, where m is the slope and b is the y-intercept of the line.

set builder notation example

{ k member of reals | k > 5 }