1 / 14

Functions

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.

eberlej
Download Presentation

Functions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Functions Section 8.1

  2. 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.

  3. Function vs. Not a Function

  4. 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)

  5. 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.

  6. Example • 3. Determine whether the graph is a function. Explain your answer.

  7. 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

  8. 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.

  9. Examples • If f(x) = 14 + 3x, find each function value: • 1. f(4)= • 2. f(-7)=

  10. 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)

  11. 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.

  12. Practice • Determine whether each relation is a function.

  13. 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.

  14. 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.

More Related