Functions and Their Graphs

These flashcards cover key concepts and definitions related to functions and their graphs as discussed in the lecture notes.

A function can be represented by a __, a graph, a numerical table, or a verbal description.

equation

The set of all possible input values for a function is called the __.

domain

The range of a function is defined as the set of all __ values of f(x) as x varies throughout D.

output

In the notation y = f(x), 'x' is the __ variable.

independent

__ is the value that depends on the input value of a function.

The output

The natural domain of a function is __ .

the largest set of real x-values for which the formula gives real y-values

The graph of a function is a useful picture of its __.

behavior

The __ of a function is the set of all points in the Cartesian plane whose coordinates are the input-output pairs for f.

graph

A function passes the vertical line test if no vertical line intersects the graph __ .

more than once

A piecewise-defined function is described in __ by using different formulas on different parts of its domain.

pieces

The absolute value function can be defined as f(x) = __ when x is greater than or equal to 0, and f(x) = -x when x is less than 0.

x

The __ of a function indicates how the function behaves as the input values increase or decrease.

monotonicity

A function is said to be increasing on an interval if __ for all x₁ and x₂ in the interval satisfying x₁ < x₂.

f(x₂) > f(x₁)

A function is called __ if f(-x) = f(x) for all values in its domain.

even

If a function is odd, then f(-x) = __ for all values in its domain.

-f(x)

The characteristic symmetry of an odd function's graph is about the __.

origin

The law of cosines states that for any triangle with sides a, b, c and angle C opposite side c, the equation is __ .

c² = a² + b² - 2ab cos(C)