COLLEGE ALGEBRA Sponsored in Part by ACEE and NSF

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COLLEGE ALGEBRA Sponsored in Part by ACEE and NSF. By Vicki Norwich and Jacci White. Activity 1. FUNCTIONS. FUNCTIONS. A function is a rule that assigns a single output to each input. Definition: A relation that assigns to each member of its domain exactly one member, its range.

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### COLLEGE ALGEBRA Sponsored in Part by ACEE and NSF

By

Vicki Norwich and

Jacci White

### Activity 1

FUNCTIONS

FUNCTIONS
• A function is a rule that assigns a single output to each input.
• Definition: A relation that assigns to each member of its domain exactly one member, its range.
• Vertical line test: If it is possible for a vertical line to intersect a graph more than once, the graph is not the graph of a function.

Functions

This example is a function because no matter where you draw a vertical line it crosses the graph no more than 1 time.

Functions

This example is not a function because if you draw a vertical line anywhere near the middle of the graph, it will cross more than one time.

Functions

This example is a function because no matter where you draw a vertical line it crosses the graph no more than 1 time.

Functions

This example is not a function because if you draw a vertical line anywhere, it will cross the graph more than one time. near the middle of

Functions

This example is a function because no matter where you draw a vertical line it crosses the graph no more than 1 time.

Functions

This example is a function because no matter where you draw a vertical line it crosses the graph no more than 1 time.

Functions

This example is not a function because if you draw a vertical line anywhere on the right side of the graph, it will cross more than one time.

Functions

DOMAIN
• The Denominator cannot equal zero. So the domain is made up of all real numbers that will not make the denominator equal to zero

Functions

• The set of all real numbers not equal to 0,4, and -3.

Functions

Domain
• An even index must have a radicand greater than or equal to zero. In other words, you cannot take an even root of a negative number.

Functions

Examples
• The following function is a square root function. Because square root is even, the part of the function under the square root sign must be greater than or equal to zero.

Functions

To find the domain of a function that has an even index, set the part under the radical greater than or equal to 0 and solve for x.

Therefore, the answer is all real numbers x>4

Solution
All rules for domains must be used whenever they apply.
• What is the domain of f(x)=x-2?
• What is the domain of g(x)=4x+7
• What is the domain of s(t)=(x+5)(x-2)?

Functions

### Solution: All real numbers

The solution is all real numbers for each of the prior three examples because there are no denominators and no radicals.