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Chapter 2 Algebra Vocab
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Terms in this set (48)
discrete
a relation in which the domain is a set of individual points
continuous
the domain of a relation has an infinite number of elements and the reaction can be graphed with a line or smooth curve
vertical line test
if a vertical line does not intersect a graph in more than one point, then the graph represents a function
domain
all X values (can't be repeated)
range
all Y values (can be repeated)
independent variable
variable whose values make up the domain in a function (usually the x)
dependent variable
function whose values depend on x (usually the y)
function notation
f(x)
linear relation
relations that have straight line graphs
linear equation
an equation that has no operations other than addition, subtraction, and multiplication of a variable by a constant (look for x, y, and =)
nonlinear relation
relations that do not have straight line graphs
linear function
a function whose ordered pairs satisfy a linear equation (f(x))
standard form
Ax+By=C where A, B, and C are integers with a greatest common factor of 1 (A is greater than or equal to 0 but A and B are not both zero)
y-intercept
the y-coordinate of the point at which a graph crosses the y-axis
x-intercept
the x-coordinate of the point at which a graph crosses the x-axis
rate of change
ratio that compares how much one quantity changes on average relative to the change in another quantity (aka slope)
slope
ratio of the change in y-coordinaets to the corresponding change in x-coordinates (rise over run) (aka rate of change)
slope intercept form
the equation of a line in the form y=mx+b where m is the slope and b is the y-intercept
point-slope form
an equation in the form y-y₁=m(x-x₁) where (x₁, y₁) are the coordinates of a point on the line and m is the slope of the line
parallel
two non vertical coplanar lines with the same slope
perpendicular
two non vertical lines that the product of their slopes is -1
Fact
The graph of a linear equation is always a line
Fact
Parallel lines have the same slope
Fact
Perpendicular lines have slopes with a product of -1 (negative reciprocal)
Fact
The slope of a vertical line is undefined
Fact
The slope of a horizontal line is 0
bivariate data
data with two variables (most of the things we graph on a coordinate plane)
scatter plot (dot plot)
a discrete set of data graphed as ordered pairs in a coordinate plane
positive correlation
slope of the line is positive /
negative correlation
slope the line is negative \
line of fit
a line that closely approximates a set of data
prediction equation
the equation of a line of fit used to predict one variable given the other other variable
piece-wise defined function
a function that is written using two or more expressions
step function
a function whose graph is a series of line segments
greatest integer function
a step function, written as f(x)=[[x]], where f(x) is the greatest integer less than or equal to x
absolute value function
a function that contains an algebraic expression within absolute value symbols, graph makes a v-shape
family of graphs
group of graphs that display one or more similar characteristics
parent graph
simplest of graphs in a family (original graph)
parent function
the simplest, most general function in a family of functions (original function)
constant function
the general equation is f(x)=a, where a is any number (domain is all real numbers and the range consists of a single real number a) (horizontal line)
identity function
f(x)=x passes through all points with coordinates (a,a) (parent function of most linear functions. domain and range are all real numbers) (y=x)
quadratic function
a function described by the equation f(x)=ax²+bx+c, where a≠0 (graph makes a parabola)
translation
moves a figure up, down, left, or right (slide)
reflection
flips a figure over a line called the line of symmetry or line of reflection (flip)
line of reflection
the line over which a reflection flips a figure
dilation
shrinks or enlarges a figure proportionally
linear inequality
resembles a linear equation, but with an inequality symbol instead of an equals symbol
boundary
a line or curve that separates the coordinate plane into two regions
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