1 / 29

Functions

This lesson explores the concept of functions, including determining if a relation is a function, using the vertical line test, finding the domain and range, and evaluating functions. Examples and practice problems are provided.

ablind
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 Warm-Up: Given f(x) = 2x – 3 what is f(-2)? What about 3f(-2)? TS: Making decisions after reflection and review

  2. Objectives • To determine if a relation is a function. • To use the vertical line test to decide whether an equation defines a function. • To find the domain and range of a function. • To use function notation to evaluate functions.

  3. Vocabulary

  4. Functions A function is a machine.

  5. Functions You put something in.

  6. Functions Information is processed.

  7. Functions You get something out.

  8. Functions PEOPLE Michael Tony Yvonne Justin Dylan Megan Elizabeth Emily BLOOD TYPE A B AB O • A function is a relation in which every element in the domain is paired with exactly one element in the range.

  9. Function? Function Function Not a Function

  10. Function? • {(1, 2), (3, 4), (5, 6), (7, 8)} Function • {(1, 2), (3, 2), (5, 6), (7, 6)} Function • {(1, 2), (1, 3), (5, 6), (5, 7)} Not a Function

  11. Vertical Line Test • If a vertical line can intersect a graph in more than one point, then the graph is not a function.

  12. Function? Function Not a Function Domain: [-3, 3] Domain: (-, ) Range: [0, ) Range: [-3, 3]

  13. Function? Function Not a Function Domain: [0, ) Domain: (-, ) Range: (-, ) Range: (-, )

  14. Function? Function Not a Function Domain: (-, 0] Domain: (-, ) Range: (-, ) Range: (-, 0]

  15. Is Y a function of X? YES! NO! YES! NO!

  16. Functions • A function pairs one object with another. • A function will produce only one object for any pairing. • A function can be represented by an equation.

  17. Functions In order to distinguish one function from another we must name it.

  18. Functions Values that go into a function are independent.

  19. Functions Values that come out of a function are dependent.

  20. Functions • To evaluate the function for a particular value, substitute that value into the equation and solve. • You can evaluate a function for an expression as well as for a number. • To do so, substitute the entire expression into the equation. • Be careful to include parentheses where needed.

  21. Functions Find what y equals when x equals 5. the machine f is a function of x that produces x - squared Find f (5)

  22. Function Notation Variable in the function Name of the function

  23. Function Notation

  24. Piece-wise Function

  25. Function Notation

  26. The Difference Quotient

  27. The Difference Quotient

  28. Composition Functions Given f(x) = 2x – 3 and g(x) = x2 but…

  29. Conclusion • A function is a relationship between two sets that pairs one object in the first set with one and only one object in the second set. • To evaluate the function for a particular value, substitute that value into the equation and solve. • To evaluate the function for an expression, substitute the entire expression into the equation; include parentheses where needed.

More Related