2.1 Functions and Their Graphs By Dr. Julia Arnold By Dr. Julia Arnold.

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Presentation transcript:

2.1 Functions and Their Graphs By Dr. Julia Arnold By Dr. Julia Arnold

A function is a rule that assigns to each element in a set A one and only one element in a set B. Domain-All elements in domain are assigned to something Range- The range consists of the elements used by the domain. The Range

In general our domain will begin with the Real Numbers. However, there are some equations which require us to use a subset of the Reals for the domain. These equations are: 1. Certain types of word problems which pertain to measurable items. For example Volume of a box in terms of the size of material. 2.Equations where the variable is in the denominator of a fraction: Equations which contain the variable under a radical: Or a combination of the above.

y = x y = x 3 y = x 2 Continued In pre-calculus you studied the graphs of some common functions

Functions continued: y = y = y =

The Vertical-Line Test shows you which graphs are functions: If you pass a vertical line across the graph it should only intersect the graph one point at a time. Non-functions:

Problem Find the domain of the function: This problem has both a radical and a fraction. We must find the numbers which keep the radicand positive and the denominator non-zero. Solution: or the denominator would be zero. In order that the radicand is positive or zero Since the domain must be greater than or equal to one, we don’t have to be concerned with -2. However, 3 is greater than 1 but must not be in the domain. So the domain is

Sketch the graph of the function with the given rule. Find the domain and range of the function. This is called a piece-wise function. It has 3 pieces. The domain is represented by the 3 if statements: x 1 which when put together is all real numbers. The first and last equation will be slanted lines. The middle equation is a horizontal line.

Problem 46 Sketch the graph of the function with the given rule. Find the domain and range of the function. The range is the set of numbers used in the graph for the y value.