Math Vocab Semester 1 Flashcards
Algebra 1
Equation
a statement that two expressions are equal.
Linear Equation
an equation that can be written in the form of ax+by=0, where a and b are constants and A doesn’t equal 0
Solution
a value that makes the equation true
Equivalent Equation
equations that have the same solution(s).
Addition Property of Equality
if you add the same number of both sides of an equation it produces an equivalent equation. If a=b than a+c=b+c
Subtraction Property of Equality
if you subtract the same number to both sides of an equation it produces an equivalent equation. If a=b, than a-c=b-c
Substitution Property of Equality
if a=b, than a can be substituted for b (or b for a) in any equation or expression
Multiplication Property of Equality
if you multiply both sides of an equation by the same nonzero number it produces an equivalent equation. If a=b, than axc=bxc, c doesn’t equal 0
Division Property of Equality
if you divide both sides of an equation by the same nonzero number it produces an equivalent equation. If a=b, then a/c=b/c, c doesn’t equal 0
Identity
an equation that is true for all values of the variable and has infinitely many solutions.
Absolute Value Equation
an equation that contains an absolute value expression.
Extraneous Solution
an apparent solution that must be rejected because it does not satisfy the original equation.
Literal Equation
an equation that has two or more variables.
Formula
a type of literal equation that shows how one variable is related to one or more other variables.
Inequality
a mathematical sentence that compares expressions using the symbols: <,>
Solution of an Inequality
is a value that makes the inequality true.
Solution Set
the set of all of the solution of an equation or inequality.
Equivalent Inequalities
are inequalities that have the same solutions.
Addition Property of Inequality
adding the same number to each side of an inequality produces an equivalent inequality.
Subtraction Property of Inequality
Subtracting the same number to each side of an inequality produces an equivalent inequality.
Multiplication and Division Properties of Inequality (c is positive)
Multiplying or dividing each side of an inequality by the same positive number produces an equivalent inequality.
Multiplication and Division Properties of Inequality (c is negative)
Multiplying or dividing each side of an inequality by the same negative number, the direction of the inequality symbol must be reversed to produce an equivalent inequality.
Compound Inequality
is an inequality formed by joining two inequalities with the word “and” or the word “or”
Intersection
of two or more sets is the set of elements that are common to every set.(The numbers that are solutions to both in equalities.)
Union
of two or more sets is the set that contains all elements of the sets. (The numbers that are solutions of either inequalities)
Set-builder Notation
uses symbols to define a set in terms of the properties of the members of the set.
Absolute Value Inequality
is an inequality that contains an absolute value expression.
Absolute Deviation
of a number x from a given value is the absolute value of the difference of x and the given value.
Relation
pairs input with outputs. A set of ordered pairs. (x,y)
Function
pairs inputs with exactly one output.
Domain
of a function is the set of all possible input values.
Range
of a function is the set of all possible output values.
Independent Variable
is the variable that represents the input values of a function and can be any value in the domain.
Dependent Variable
is the variable that represents the output values because it depends on the value of the independent variable.
X-intercept
of a graph is the x-coordinate of a point where the graph intersects the x-axis. It occurs when y=0.
Y-intercept
of a graph is the y-coordinate of a point where the graph intersects the y-axis. It occurs when x=0
End Behavior
of a function is the behavior of the graph as x approaches positive infinity or negative. A function is positive when its graph lies above the x-axis. A function is negative when its graph lies below the x-axis. A function is increasing when its graph moves up as x moves to the right. A function is decreasing when its graph moves down as x moves to the right.
Linear Equation in Two Variables
x and y, is an equation that can be written in the form y=mx+b whre m and b are constants.
Linear Function
is a function whose graph is a nonvertical line.
Nonlinear Function
is a function that does not have a constant rate of change. So, its graph is not a line.
Discrete Domain
is a set of input values that consist of only certain numbers of an interval.
Continuous Domain
is a set of input values that consists of all numbers of an interval.
Function Notation
use f(x) instead of y to quickly identify which variable is the independent variable.
Standard Form
of a linear equation is Ax+By=C, where, A,B and C are real numbers and A and B are not both 0, and A,B and C are integers that don’t have any common factors other than 1 and A>1.
Slope
is the rate of change between any two points on a line. It measures the steepness of the line.
Constant Function
a linear equation written in the form y=0x+b, or y=b. The graph of a constant function is a horizontal line.
Reflection
flips a graph over a line called the line of reflection. The graph of y=-f(x) is a reflection in the x-axis of the graph of y=f(x). y=f(-x) is a reflection in the y-axis of the graph of y=f(x)
Horizontal Stretch
transforming a function by multiplying all the inputs (x-coordinates) by the same factor a. When 0<a<1.
Horizontal Shrink
a transforming a function by multiplying all the inputs (x-coordinate) by the same factor a. When a>1.
Vertical Stretch
a transforming a function by all the outputs (y-coordinates) by the same factor a. When a>1.
Vertical Shrink
a transforming a function by multiplying all the outputs(y-coordinates) by the same factor a. When 0<a<1
Absolute Value Function
is a function that contains an absolute value expression. Its graph is v-shaped and symmetric about the y-axis. The vertex is the point where the graph changes direction.
Linear Model
is a linear function that models a real-life situation.
Point-Slope Form
a linear equation written in the form y-y1=m(x-x1)
Parallel lines
two lines in the same plane that never intersect. They are lines that have the same slope and a different y-intercept.
Perpendicular Lines
intersect to form a right angle. Their slopes are opposite reciprocals and have a product of negative one.
Scatter Plot
a graph that shows the relationship between two data sets. The two data sets are graphed as ordered pairs in a coordinate plane.
Correlation
is a relationship between data sets. You can use a scatter plot to describe correlation between data.
Positive Linear Correlation
the points lie close to a line As x increases, y increases
Negative Linear Correlation
the points lie close to a line. As x increases, y decreases.
No correlation
the points show no pattern.
Line of best fit
is a line drawn on a scatter plot that is close to most of the data points.
Causation
is when a change in one variable causes a change in another variable.
Interpolation
using a graph or its equation to approximate a value between two known values.
Extrapolation
using a graph or its equation to predict a value outside the range of known values.
System of linear equations
is a set of two or more linear equations in the same variables.
Linear Inequality in Two Variables
x and y, can be written in one of the following forms, where a, b, and c are real numbers.
Solution of a Linear Inequality in Two Variables
is an ordered pair (x,y) that makes the inequality true.
Graph of a Linear Inequaltiy
in two variables shows all the solutions of the inequality in a coordinate plane. A dashed boundary line means that points on the line are not solutions. A solid boundary line means that point on the line are solutions.
Half-plane
the boundary line divides the coordinate plane into two half-planes.
System of Linear Inequalities
is a set of two or more linear inequalities in the same variables.
Solution of a System of linear Inequalities
in two variables is an ordered pair that is a solution to each inequality
Graph of a System of Linear Inequalities
is the graph of all the solutions of the system.
