absolute value function
a function that contains an absolute value expression
constant function
a linear equation written in the form y = 0x + b, or y = b
continuous domain
a set of input values that consist of all numbers in an interval
dependent variable
the variable that represents output values of a function
discrete domain
a set of input values that consists of only certain numbers in an interval
domain
the set of all possible input values of a function
family of functions
a group of functions with similar characteristics
function
a relation that pairs each input with exactly one output
function notation
another name for y denoted as f(x) and read as “the value of f at x” or “f of x”
horizontal shrink
a transformation that causes the graph of a function to shrink toward the y-axis when all the x-coordinates are multiplied by a factor a, where a > 1
horizontal stretch
a transformation that causes the graph of a function to stretch away from the y-axis when all the x-coordinates are multiplied by a factor a, where 0 < a < 1
independent variable
the variable that represents the input values of a function
linear equation in two variables
an equation that can be written in the form y = mx + b, where m and b are constants
linear function
a function whose graph is a nonvertical line
nonlinear function
a function that does not have a constant rate of change and whose graph is not a line
parent function
the most basic function in a family of functions
range of a function
the set of all possible output values of a function
reflection
a transformation that flips a graph over a line called the line of reflection
relation
a pairing of inputs with outputs
rise
the change in y between any two points on a line
run
the change in x between any two points on a line
slope
the rate of change between any two points on a line
slope-intercept form
a linear equation written in the form y = mx + b
solution of a linear equation in two variables
an ordered pair (x, y) that makes an equation true
standard form of a linear equation
a linear equation written in the form Ax + By = C, where A, B, and C are real numbers and A and B are both not zero
transformation
a change in the size, shape, position, or orientation of a graph
translation
a transformation that shifts a graph horizontally and/or vertically but does not change the size, shape, or orientation of the graph
vertex
the point where a graph changes direction
vertex form of an absolute value function
an absolute value function written in the form f(x) = a
vertical shrink
a transformation that causes the graph of a function to shrink toward the x-axis when all the y-coordinates are multiplied by a factor a, where 0 < a < 1
vertical stretch
a transformation that causes the graph of a function to stretch away from the x-axis when all the y-coordinates are multiplied by a factor a, where a > 1
x-intercept
the x-coordinate of a point where the graph crosses the x-axis
y-intercept
the y-coordinate of a point where the graph crosses the y-axis