Following are the key features of functions. 1. Domain and Range. 2. x-intercept and y-intercept. 3. Positive and Negative intervals. 4. Intervals of increasing, decreasing and constant behavior. 5. Parent Functions. 6. Maxima and Minima. Domain : The domain is the set of all possible inputs or x …

By definition: A function is strictly increasing on an interval, if when x1 < x2, then f (x1) < f (x2). If the function notation is bothering you, this definition can also be thought of as stating x1 < x2 implies y1 < y2. As the x 's get larger, the y 's get larger.

We say “the output is a function of the input.” The input values make up the domain, and the output values make up the range. How To: Given a relationship between two quantities, determine whether the relationship is a function. Identify the input values.

Identify functions given in tabular form. Write and evaluate functional relationships using standard notation. Determine whether a function is one-to-one. A relation is a set of ordered pairs.

Given a function in a table or in algebraic or graphical form, identify key features such as x- and y-intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; and end behavior.

In this section, we provide a formal definition of a function and examine several ways in which functions are represented—namely, through tables, formulas, and graphs. We study formal notation and terms related to functions. We also define composition of …

In table form, a function can be represented by rows or columns that relate to input and output values. To evaluate a function we determine an output value for a corresponding input value. Algebraic forms of a function can be evaluated by replacing the input variable with a given value.

What are the characteristics of a function? A function is a special type of relation between two sets, typically known as the domain (input) and the range (output). A function has the following characteristics: Characteristic 1: Each element in the domain …

DEFINITION 1: A function consists of two nonempty sets X and Y, and a rule f that associates each element x in X with one and only one element y in Y. This is symbolized by f : X → Y and read “the function f from X into Y.” This phrase is often shortened to “the function f.”

Students are introduced to the main features of functions that they will learn throughout the year, providing students with a conceptual understanding of how functions are used to model various situations.