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Level 362

Linear Relations & Functions


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one-to-one function
A function where each element of the range is paired with exactly one element of the domain.
onto function
Each element of the range corresponds to an element of the domain.
continuous relation
A relation that can be graphed with a line or smooth curve.
discrete relation
A relation in which the domain is a set of individual points.
VERTICAL LINE TEST
A line is a function is it passes the
standard form
A linear equation written in the form Ax+By=C, where A, B, and C are integers whose greatest common factor is 1, A ≥ 0, and A and B are not both zero.
slope
(y₂-y₁)/(x₂-x₁)
parallel lines
2 lines that never cross/intersect and stay the same distance apart
perpendicular
two lines that intersect and form a right angle are
family of graphs
A group of graphs that displays one or more similar characteristics.
y-intercept
the point where the line crosses the y-axis
x-intercept
the point where the line crosses the x-axis
Absolute Value Function
any f(x) = | x |
bivariate relation
Data with two variables.
correlation coefficient
If σ₁ and σ₂ are the variances of Y₁ and Y₂, the correlation coefficient is:
*dependent variable
The other variable in a function, usually y, whose values depend on x.
Dilation
a transformation that changes the size of an object, but not the shape
direct variation
If gummy bears cost $3.50 per pound, how much will 6 pounds cost? How much would a half a pound cost?
greatest integer function
A step function written as f(x)= [x], where f(x) is the greatest integer less than or equal to x.
independent variable
the tested varaible
Linear Equation
A polynomial equation of the first degree whose graph is a line.
Linear Function
y = mx + b
linear inequality
contains a single variable on either side of the inequality symbol.
line of fit
A line that closely approximates a set of data.
negative correlation
y tends to decrease, as x increases
Parent Function
the most basic function of a family of functions, or the original function before a transformation is applied
piecewise-defined function
A function that is written using two or more expressions.
point-slope form
Given a point (x₁, y₁) and slope m
positive correlation
y tends to increase, as x increases
prediction equation
An equation suggested by the points of a scatter plot that is used to predict other points.
Quadratic Function
a function that can be written in the form f(x)=ax^2+bx+c, where a, b & c are real numbers and a is not equal to zero
Rate of change
A value that results from dividing the change in a function (y-values) of a variable by the change in the variable (x-values). It is another name for slope.
reflection
It is a transformation that flips a figure over a line of reflection.
regression line
predicts the value for the response variable y as a straight line function of the value x of the explanatory variable
Scatter plot
is a graph used to determine whether there is a relationship between paired data. Scatter plots can show trends in data.
Slope-Intercept Form
a linear equation written in the form y = mx + b, where m represents slope and b represents the y-intercept
step function
A function whose graph is a series of line segments.
translation
It is a transformation that moves points the distance and in the same direction.