math 3 Semester 1 Function Overview

An Absolute Value Function is a function that outputs the non-negative value of its input. It is defined as f(x) = |x|, which means that f(x) = x if x >= 0 and f(x) = -x if x < 0.

The general form of a Quadratic Function is f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

A Cubic Function is a polynomial function of degree three, typically expressed in the form f(x) = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants and a ≠ 0.

A Logarithmic Function is the inverse of an exponential function, defined as f(x) = log_b(x), where b is the base of the logarithm.

Inverse functions reflect over the line y = x.

The general form of an Exponential Function is f(x) = ab^x, where a is a constant, b is the base, and x is the exponent.

A Rational Function is a function that can be expressed as the ratio of two polynomials, typically in the form f(x) = P(x)/Q(x), where P and Q are polynomials.

The graph of an Absolute Value Function forms a 'V' shape, opening upwards.

The graph of a Quadratic Function is a parabola, which can open upwards or downwards depending on the sign of the coefficient a.

The graph of a Cubic Function can have one or two turning points and can extend to positive or negative infinity.