Algebra 2 vocabulary & definitions

A number’s distance from zero on the number line, written $\lvert x\rvert$. Absolute value is never negative.

The change in output over an interval divided by the change in input: $\frac{f(b)-f(a)}{b-a}$, where $a\ne b$. It is the slope of the secant line through the endpoints.

A number multiplying a variable or variable expression. In $-3x$, the coefficient of $x$ is $-3$.

Two inequalities joined by “and” or “or.” An “and” solution must satisfy both; an “or” solution satisfies at least one.

A value that does not change in the expression or situation being considered.

A statement that cannot be true. If solving an equation produces $0=5$, the original equation has no solution.

Multiplying a sum by a number gives the same result as multiplying each term: $a(b+c)=ab+ac$.

The set of all allowed input values of a function or relation.

A statement that two expressions have the same value.

Numbers, variables, and operations combined without an equality or inequality statement.

A candidate answer produced during solving that does not satisfy the original problem; checking rejects it.

An equation expressing a relationship among quantities, such as $A=lw$.

A relationship assigning exactly one output to each input in its domain. Different inputs may have the same output.

Notation such as $f(x)$ for the output of function $f$ at input $x$. It means a function value, not $f$ multiplied by $x$.

An equation true for every value in its domain, such as $2(x+1)=2x+2$.

A comparison using $<$, $>$, $\leq$, or $\geq$. Multiplying or dividing both sides by a negative number reverses the inequality sign.

A value supplied to a function; usually represented by the independent variable $x$.

Values common to both sets; used for an “and” compound inequality.

A way to describe sets of real numbers with endpoints. Parentheses exclude an endpoint; brackets include it. Infinity always uses a parenthesis.

Operations that undo each other, such as addition and subtraction, or multiplication and division by the same nonzero number.

Terms with exactly the same variable factors and exponents. For example, $3x$ and $-2x$ are like terms.

An equation whose graph is a straight line, such as $Ax+By=C$, where $A$ and $B$ are not both zero.

A straight-line relationship used to represent a situation with a constant rate of change and a starting value.

The agreed order for evaluating expressions: grouping, exponents, multiplication and division from left to right, then addition and subtraction from left to right.

Two numbers $(x,y)$ identifying a point: the first gives horizontal position and the second gives vertical position.

The value produced by a function for a given input; often written $y$ or $f(x)$.

A rule that keeps an equation true when the same number is added to, subtracted from, or multiplied on both sides, or both sides are divided by the same nonzero number.

The set of all output values actually produced by a function or relation.

The change in one quantity divided by the corresponding change in another, with units such as dollars per hour. A line has a constant rate of change equal to its slope.

For a nonzero number $a$, the number $\frac{1}{a}$. Their product is 1.

The change in y divided by the corresponding nonzero change in x: $m=\frac{y_2-y_1}{x_2-x_1}$. Vertical lines have undefined slope; horizontal lines have slope zero.

The equation $y=mx+b$, where $m$ is the slope and $(0,b)$ is the y-intercept. Vertical lines cannot be written in this form.

A value that makes an equation or inequality true when substituted for the variable.

All values that make a statement true.

Replacing a variable or expression with an equal value or expression.

A part of an expression separated by addition or subtraction. In $3x-5$, the terms are $3x$ and $-5$.

Values in either set or both; used for an “or” compound inequality.

A letter or symbol that represents a number whose value may vary or be unknown.

A point where a graph meets the y-axis, so $x=0$.