Precalculus I: Functions Learning Targets

Flashcards created from lecture notes on the learning targets for Precalculus I, focused on key concepts and definitions relevant to functions.

Function

A relation where each input has exactly one output.

Domain

The set of all possible input values for a function.

Range

The set of all possible output values of a function.

Intercepts

Points where a graph intersects the axes (horizontal and vertical intercepts).

Average Rate of Change

The change in the function's value over the change in the input value over an interval.

Composition of Functions

Combining two functions where the output of one function becomes the input of another.

Transformations

Changes made to the graph of a function that affect its position, shape, or size.

Inverse Function

A function that reverses the effect of the original function.

Quadratic Function

A function that can be described by a polynomial of degree two (ax^2 + bx + c).

End Behavior

A description of the behavior of a function as x approaches positive or negative infinity.

Polynomial Function

A function that can be represented as a polynomial equation.

Factoring

Breaking down a polynomial into simpler components, usually to find its zeroes.

Rational Function

A function expressed as the ratio of two polynomials.

Asymptote

A line that a graph approaches but never touches.

Exponential Function

A function in which an independent variable is in the exponent.

Logarithmic Function

The inverse of an exponential function, expressing the power to which a base must be raised to obtain a certain number.

Change-of-Base Formula

A formula used to rewrite logarithms in terms of logarithms of a different base.

Contextualized Problem

A problem that applies mathematical concepts to real-world situations.

Synthetic Division

A simplified method of dividing polynomials.

Zeros of a Function

Values of x that make the function equal to zero.