algebra 1 eoc

relation

set of ordered pairs

ordered pair

the x and y coordinates of a point on the coordinate plane

coordinate plane

a plane formed by 2 perpendicular lines called axes

function

special relation where each x-value is paired with ONLY ONE y-value. (x-values DO NOT repeat, it passes the vertical line test)

domain

set of all of the possible x-values. INPUTS

range

set of all the possible y-values. OUTPUTS

variable

NOT A NUMBER. A letter or symbol that stands for a number. Variables vary or change

independent variable

the INPUT or CAUSE in a situationor proble,m. It's the variable YOU CAN control. It's the X variable.

dependent variable

the OUTPUT or RESULT in a situation or problem. It's the variable YOU CANNOT control. It's the Y variable. In a equation, its the variable BY ITSELF on one side of the = sign.

other names for "x"

domain, independent variable, input

other names for "y"

range, dependent variable, output

vertical line test

a relation is a function and passes the vertical line test if when a vertical line is drawn through the graph, it touches the graph only ONE time.

discreet function

data appears as individual point on a graph. Whatever is being graphed cannot be broken down in to smaller pieces......like stairs or people.

continuous function

data appears as a smooth curve on a graph. Whatever is being graphed can be broken down in to smaller pieces......like time.

graph of a linear function

graph of a quadratic function

graph of an inverse function

graph of exponential decay function

graph of exponential growth function

words for "<"

less than, is smaller than, below

words for ">"

more than, is greater than, is larger than, above

in y = mx + b, "m" stands for?

slope

in y = mx + b, "b" stands for?

the y-intercept

changing the "m" in the slope-intercept form of the equation of a line changes what?

the steepness of the line

changing the "b" in the slope-intercept form of the equation of a line changes what?

moves the line up or down the y-axis.

what is the linear parent function?

y = x

define slope

the steepness of a line, vertical change/horizontal change

how is slope important for linear equations and lines?

linear equations and lines have CONSTANT slopes. The slope is the SAME all the way up and down the line.

what slope does a HORIZONTAL line have?

slope = 0

what slope does a VERTICAL line have?

undefined slope

what is the x-intercept?

the point where the graph crosses the x-axis. It has the coordinates (x, 0)

what is the y-intercept?

the point where the graph crosses the y-axis. It has the coordinates (0, y)

What is Direct Variation?

y = mx, or y = ax, or y = kx. m, a, or k is just the coefficient in front of the x. They are also the SLOPE of the direct variation line. Direct variation lines have a y-intercept ot (0, 0)

What is Inverse Variation?

y = 1/x. As one quantity increases, the other decreases

what is a linear inequality?

It is an equation with a

How do the slopes of parallel lines compare?

They are the same

How do the slopes of perdendicular lines compare?

They are opposite and fraction is flipped. Example: lines with the slopes -2 and 1/2 are perpendicular.

What is a line of best fit?

A line drawn through the points on a scatterplot to estimate the best line through the data.

What is a system of equations?

2 or more equations graphed on the same coordinate plane

What is the SOLUTION of a system of equations?

where the lines touch or cross

How many solutions can a system 2 equations have?

1. no solutions, if the lines are parallel and have the same slope. 2) one solution, if the lines intersect at one point. 3) infinite many solutions, if the two equations are the same and touch each other everywhere.

What is a quadratic equation or function?

an equation of function that has "x-squared" as its highest order exponent. Example: 2x^2 + x + 3

Where are the solutions of a quadratic function?

at the x-intercepts. They are also known as zeros and roots.

What are "like terms"?

mathmatical terms that have the SAME variables raised to the SAME exponents.

How do you combine like terms?

Add their coefficients.

How do you MULTIPLE exponents of like variables?

ADD them

How do you DIVIDE exponents of like variables?

SUBTRACT them

What is the "rate of change" on a graph?

Slope