Algebra Chpt 2

function rule

represents an output value in terms of an input value

parallel lines

coplanar lines that do not intersect. In the coordinate plane, parallel lines have the same slope.

Relationship

A set of ordered pairs. Example: {(0,1), (0,2), (0,3), (0,4), (14)}

boundary

A boundary of the graph of a linear inequality is a line in the coordinate plane. It separate the solution of the inequality from the non solutions. Points of the line itself may or may not be solutions

linear function

A function whose graph is a line is a linear function. You can represent a linear function with a linear equation.

absolute value function

A function written in the form f(x) =|mx+b| + c, where m not equal 0, is an absolute variable. Example f(x)= |3x-2| + 3 ; f(x)=|2x|

Scatterplot

A graph that relates the two different sets of data by plotting the data as ordered pairs. You can use a scatter plot to determine a relationship between the data sets.

axis of symmetry

A line that divides a figure in half so that each half is the mirror image of the other

Transformation

A transformation of a function y = af (x - h) is a change made to at least one of the values a,h, and K. The four types of transformations are dilations, reflections, rotations and translations. Example: g(x) = 2(x-3) is a transformation of f(x) = x

Translation

A translation shifts the graph of the parent function horizontally, vertically or both without changing its shape or orientation

independent variable

An equation using the variables x and y, where x represents input value, then x is the independent variable. Example y = 2x + 1; x is the independent variable

linear inequality

An inequality in two variables whose graph is a region of the coordinate plane that is bounded by a line.

standard form of a linear equation

Ax + By = C, where A,B, and C are real numbers, and A and B are not both zero.. y =4/3 x -1 is 4x + (-3)y = 3

Reflection

Flips the graph of a function across a line, such as the x or y axis. Each point on the graph of the reflected function is the same distance from the line of reflection as is the corresponding point on the graph of the original function.

dependent variable

If a function is defined by an equation using the variables x and y, where y represent output values, then y is the dependent variable.

function notation

If x is the independent variable and y is the dependent variable, then the function notation for y is f(x), read "f of x," where f names the function.

linear equation

In two variable is an equation that can be written in the form ax+by=c. See also Standard form of a linear equation. Example y = 2x + 1 can be written as -2x + y = 1

Correlation

Indicates the strength of a relationship between two data sets.

perpendicular lines

Lines that intersect to form right angles. In the coordinate plane, perpendicular lines have slopes with product -1. Two lines are perpendicular if the product of their slopes is -1.

range

Set of all outputs or y-coordinates of the ordered pairs. Example in the relation {(0,1), (0,2), (0,3), (0,4), (1,3), (1,4), (2,1)}, the range is the set of real numbers greater than or equal to zero.

slope

Slope of a non vertical line is the ratio of the vertical change to the horizontal change between points. You can calculate slope by finding the ratio of the difference in the y- coordinates to the difference in the x-coordinates for any two points on the line. The slope of the line through points (-1, -1) and (1, -2) is -2-(-1)/1-(-1) = -1/2 = 1/2

constant of variation

The constant of variable is the ratio of the two variables in a direct variable and the product of the two variables in an inverse variation. Example: In y=3.5x, the constant of the variation K is 3.5; in xy=5, the constant of variable K is 5

correlation coefficient

The correlation coefficient, r, indicates the strength of the correlation. The closer r is to 1 or -1, the more closely the data resembles a line and the more accurate your model is likely to be

Domain

The domain of a relation is the set of all inputs or x-coordinates of the order pairs. Example: in the relation {(0,1)(0,2)(0,3)(0,4)(1,3)(1,4)(2,1)} the domain is {0,1,2}. In the function f(x) = x square - 10, the domain is all real number.

slope intercept force

The slope intercept form of an equation of a line is y=mx+b, where m is the slope and b is the y-intercept. Example: y = 8x + 2, y = -x +1, y = -1/2 x - 14

Test Point

a point you pick on one side of the boundary of the graph of a linear inequality; if the test point makes the inequality true, all the points on that side of the boundary are solutions. If the test point makes the inequality false, then all points on the other side are solutions.

direct variation

a linear function defined by an equation of the form y=kx, where k does not equal 0, represents direct variation. Example: y=3.5x, y=7x, y=-1/2x

Function

a relation in which each element of the domain corresponds with exactly one element of the range. Example: the relation y=3x3-2x+3 is a function f(x)=3x3-2x+3 is the same relation written in function form

Half-plane

the set of points in a coordinate plane that are on one side of the boundary of the graph of a linear inequality

parent function

the simplest form of a set of functions which form a family. Example: y=x is the parent function of the form y=x+k

line of best fit

the trend line that gives the most accurate model of related data is the line of best fit

point slope form

y-y₁=m(x-x₁) where m is the slope and (x₁, y₁) is a point on the line. Example: y-3 = 2(x-1), y+4 = 5(x-2, y-2 = 3(x+2)