Functions SECTION 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 EquationFunction Notation y = 2x + 3f(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) = x, 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.