FunctionsSECTION 8.1

Notes: Relations and Functions

The ________________ is a value that does not depend upon another variable.

The _________________ is a value that depends on the input value.

Recall that functions are _________ in which each element of the domain is paired with __________ one element of the range.

Function vs. Not a Function

Examples

Determine whether each relation is a function. Explain.

1. (5,1), (6,3), (7,5), (8,0)

2. (54,112), (56,130), (55,145), (54,123), (56,128)

Notes: Relations and Functions

Another way to determine whether a relation is a function is to apply the ___________ to the graph of the function.

If, for each value of x in the domain, a vertical line passes through no more than one point on the graph, then the graph represents a function.

If the line passes through more than one point on the graph, it is not a function.

Example 3. Determine whether the graph is a function.

Explain your answer.

Notes: Function Notation

A function that is written as an equation can also be written in a form called ____________.

Consider the equation y = 2x + 3

Equation Function Notation

y = 2x + 3 f(x) = 2x + 3

Notes: Function Notation

The variable y and f(x) both represent the _________ variable.

In the example above, when x = ____, f(x) = ____

In function notation, f(x) is read “f of x” and is equal to the value of the function at x.

Examples

If f(x) = 14 + 3x, find each function value:

1. f(4)=

2. f(-7)=

Notes: Describe Relationships

A function can also describe the relationship between two quantities.

For example, the distant you travel in a car depends on how long you are in he car.

In other words, distance is a function of time or d(t)

Example 1. A whale watching boat traveled at a sped of 5.5 miles

per hour.

A. Identify the independent and dependent variables. Then write a function to represent the total distance traveled in any number of hours spent whale watching.

B. Use the function to find how long it took to travel 25 miles. Round to the nearest tenth.

Practice

Determine whether each relation is a function.

H.O.T. Problems

38. Draw two graphs, one that represents a relation that is a function and one that represents a relation that is not a function. Explain why each graph is or is not a function.

H.O.T. Problems

46. How can the relationship between water depth and time to ascend to the water’s surface be a function?

Explain how the two variables are related. Discuss whether water depth can ever correspond to two different times.