1 / 16

Chapter 1 Introducing Functions

Chapter 1 Introducing Functions. Definition (page 13) A function is a relationship between two sets, the domain and the range, such that each member of the domain corresponds to exactly one member of the range. The domain is the set of inputs that make sense for the function

nevaeh
Download Presentation

Chapter 1 Introducing 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. Chapter 1 Introducing Functions

  2. Definition (page 13) A function is a relationship between two sets, the domain and the range, such that each member of the domain corresponds to exactly one member of the range. The domain is the set of inputs that make sense for the function The range is the set of outputs that can be expected from the function.

  3. Section 1.1 – Defining Functions A function can be expressed using: Formula Table Graph #1 Shoe Size #2 River Level #3 Z function

  4. Example 1 – Shoe Size(formula) Your shoe size is certainly related to the size of your foot. In fact, a shoe salesperson might say that your shoe size “is a function of” or “depends on” the length of your foot. For a woman’s foot, we use the following formula which tells specifically how to convert x, the length in inches of a woman’s foot, into y, the number giving her shoe size: y = 3x – 21 (or S = 3L – 21) (In words, measure the length of a woman’s foot in inches, multiply this measurement by 3 and subtract 21.) For a man’s foot, we use the following formula which tells specifically how to convert x, the length in inches of a man’s foot, into y, the number giving his shoe size: y = 3x – 22.5 (or S = 3L -21) (In words, measure the length of a man’s foot in inches, multiply this measurement by 3 and subtract 22.5.)

  5. Example 1 – Shoe Size (formula) Function Notation y = 3x -21 w(x) = 3x - 21 y = 3x - 22.5 m(x) = 3x – 22.5 Allows us to refer to function by name. Emphasizes the role of the input/output variables. w(9)=6 A woman whose foot measures 9 inches wears a size 6 shoe

  6. Example 1 – Shoe Size (table) Create a table of values for w. Create a table of values for m.

  7. Example 1 – Shoe Size (graph) Graph the shoe size functions w and m.

  8. Example 2 – River Level (table) Function Notation x variable: day in April y variable: river level (in feet above sea level) C(x) C(10)= 111.1 The river level on April 10 was 111.1 feet above sea level

  9. Example 2 – River Level (graph)

  10. Example 2 – River Level (graph) C(14.5) = 113

  11. Example 3 – Z function (graph) What is Z(4)? What is Z(0)? For what input values does Z(u) = 10?

  12. Section 1.2Using Functions to Model the Real World Consider w(x) = 3x – 21. Domain: all real numbers Range: all real numbers Domain: legal foot measurements? Range: legal shoe sizes?

  13. Section 1.2Using Functions to Model the Real World Consider w(x) = 3x – 21. discrete Range (legal women’s shoe sizes): {5, 5.5, 6, 6.5, 7, 7.5, 8, 8.5, 9, 9.5, 10, 10.5, 11, 11.5,12, 12.5, 13} Domain (legal women’s foot measurements): 5 ≤ 3x – 21 ≤ 138.66 inches ≤ x ≤ 11.33 inches continuous

  14. Section 1.2 – Using Functions to Model the Real World Examples from pages 12 and 13

  15. Definition (page 13) A function is a relationship between two sets, the domain and the range, such that each member of the domain corresponds to exactly one member of the range. The domain is the set of inputs that make sense for the function The range is the set of outputs that can be expected from the function. Example (pp14/15): Input: square of a number. Output: number that was squared to get the input.

  16. More Practice 11/32, 12/32 and 24/33 Homework: Page 31: #1-24 Turn in: 14, 16, 20,24

More Related