Precalculus Complete Study Guide

Vocabulary flashcards covering key concepts from Precalculus functions, transformations, graph behavior, function operations, quadratics, polynomials, rational functions, logarithms, and exponential models.

Function

Each x has exactly one y.

Vertical line test

Determines if a graph is a function.

Domain rules

Denominator cannot be zero, square root must be nonnegative, log must be positive.

x intercepts

Found by setting y equal to zero.

y intercept

Found by plugging in x equals zero.

Transformations

Operations that shift, reflect, or change the graph of a function.

Increasing graph

Graph rises from left to right.

Decreasing graph

Graph falls from left to right.

Maximum

The highest point on a graph.

Minimum

The lowest point on a graph.

Even symmetry

Graph mirrors over the y axis.

Odd symmetry

Graph mirrors over the origin.

Function operations

Combine functions using addition, subtraction, multiplication, and division.

Composition of functions

Plugging one function into another.

Vertex of a quadratic

x coordinate calculated as -b divided by 2a.

Discriminant

Indicates the number of solutions of a quadratic.

Polynomial degree

The highest exponent in a polynomial.

Even multiplicity of roots

Bounces off the x-axis at x intercepts.

Odd multiplicity of roots

Crosses the x-axis at x intercepts.

Rational functions

Functions defined as the ratio of two polynomials.

Vertical asymptotes

Vertical lines where the denominator is zero.

Holes in rational functions

Points where factors cancel in the function.

Logarithm definition

log_b(x)=y means b^y=x.

Product rule for logs

Adds logs when multiplying.

Quotient rule for logs

Subtracts logs when dividing.

Power rule for logs

Brings the exponent down in log expressions.

Exponential growth model

When the base is greater than 1.

Exponential decay model

When the base is between 0 and 1.