AP Precalculus Terms & Formulas

Function

A mathematical relation that maps input values to output values, where the input values are the domain and the output values are the range.

Inflection Point

The point on a curve where the concavity changes from up to down or down to up.

x-intercepts

The solutions of f(x)=0, represented as (x,0) on the graph.

y-intercepts

The value of f(0) or (0,y) on the graph of a function.

Average Rate of Change (AROC)

The slope between two points on a graph of f(x).

Instantaneous Rate of Change

The rate at which y-values change when x-values change at a specific point.

Polynomial Function

A monomial or a sum of monomials.

Turning Point

A point where the function changes direction.

End Behavior

The direction of the function's graph as you move away from the origin.

Relative/Local Extrema

Points where the function changes from increasing to decreasing or vice versa.

Absolute/Global Extrema

The highest or lowest y-values on the graph.

Odd Function

Travels through the origin and follows f(-x)=-f(x).

Even Function

Reflects over the y-axis and satisfies f(-x)=f(x).

Imaginary Number

A number where the root is imaginary when the radicand is negative.

Complex Number

A number of the form a+bi where a is the real part and bi is the imaginary part.

Complex Conjugate

If (a+bi) is a factor, then (a-bi) is also a factor.

If a residual is negative, the model is an:

overestimate

If a residual is positive, the model is an:

underestimate

formula to find a residual:

ACTUAL - PREDICTED (“AP”)

If a data model is appropriate:

the residual plot should appear without a pattern

If a data model is not appropriate:

the residual plot appears to have a pattern