Nomials
Binomials
an algebraic expression with two different variables separated by a + or -
When you have an exponent raised to another exponent you keep the base and multiply the exponents.
The power to a power rule
Domain
The set of all inputs of a function (the x-values or independent variables).
Interval notation
A notation for describing an interval on a number line. The interval's endpoint(s) are given, and a parenthesis or bracket is used to indicate whether each endpoint is included in the interval.
Roots
Another name for x-intercepts
Monomials
An algebraic expression consisting of one term.
When multiplying two terms with the same base, keep the base the same and add the exponents together.
The Product Rule of Exponents
Range
The set of output values of a function (the y-values or dependent variables).
Relative maximum/minimum
The y-coordinate of any point that is the highest/lowest point for some section of the graph
Quadratic Function
A function in which the greatest power of the variable is 2.
Trinomials
An algebraic expression with three different variables separated by a + or -
Negative exponent rule
A negative exponent is defined as the multiplicative inverse of the base, raised to the power which is of the opposite sign of the given power.
Vertical line test
A test used to determine whether a relation is a function by checking if a this line touches 2 or more points on the graph of a relation.
Inverse Function
A function that "undoes" what the original function does.
Zeros (in a function)
Another name for x-intercepts.
Polynomial
an expression of 1 or more algebraic terms that can be separated by a + or -
Zero as an exponent
Any number (except zero) raised to the power of 0 is 1.
One to one function
A function for which every y-value of the function corresponds to exactly one x-value.
Inverse Function Notation
If a function y = f(x) has an inverse that is also a function we represent as y = f^-1 (x)
Direct variation
he relationship between two variable quantities that have a constant ratio.
Algebraic Expressions
These just combinations of constants and variables using the typical operations of addition, subtraction, multiplication, and division along with exponents and roots (square roots, cube roots, etcetera).
The Quotient Rule of Exponents
When you are dividing and the bases are the same then keep the same base and subtract the exponents.
Domain Restriction
A limitation on the domain of a function, usually to represent only values that are realistic in a given context.
Examples include: Not dividing by 0 (or having it in the denominator) and not having a negative underneath a square root.
Existence of Inverse Functions
A function will have an inverse that is also a function if and only if it is one-to-one. Hence a quick way to know if a function has an inverse that is also a function is to apply the Horizonal Line Test.
Proportional or Direct Relationship
Two variables, x and y have a direct (proportional) relationship if for every ordered pair (x, y) we have:
y/x = k or y = k*x
Stated simply, y will always be a constant multiple of x. The value of k is known as the constant of variation.