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Functions

Learn about functions, domains, and ranges. Discover how to determine if a graph represents a function, create mappings, and graph different types of functions like linear and quadratic. Practice with examples and improve your graphing skills!

jeffrodriguez
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Functions

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  1. Functions Chapter 4

  2. What makes a graph a function? • The graph passes the vertical line test Passes Fails

  3. What makes a graph a function? • Each domain (x-value) is mapped to only one range (y-value). • We create a “mapping” to see if a relation (set of ordered pairs) is a function.

  4. Domain & Range • Domain: all x-values • List in braces from least to greatest and do not repeat values • Range: all y-values • List in braces from least to greatest and do not repeat values

  5. Domain & Range Example {(3, 4), (-2, 7), (9, 10), (9, 11)} Domain {-2, 3, 9} Range {4, 7, 10, 11}

  6. Mapping Diagram NOT A FUNCTION: FUNCTION: (4, 5), (4, -3), (-1, 2), (6,0) (4, 5), (-2, 7), (3, 7), (0, -1) -3 -2 -1 -1 0 0 4 5 2 3 6 7 5 4 Try using the vertical line test…does the relation pass?

  7. Make a Table, Mapping, & Graph {(9, 2), (-3, 4), (1, 5), (-1, 2)} Table Mapping Graph

  8. Types of Functions • Linear • Quadratic • Absolute Value • Exponential • Cubic

  9. Let’s GRAPH! • Create a T-Chart x y

  10. Graphing Continued: • Pick values for x. • Plug in x and use PEMDAS to solve for y. • Plot ordered pairs. • Connect the points. • Include arrows at the end of your line. • CHECK your work 

  11. Try these linear functions: • y = 3x + 1 • y = -2x + 3 • y = x – 4 What patterns do you see between the equations and the graph?

  12. Functions Chapter 4

  13. What makes a graph a function? • The graph passes the vertical line test Passes Fails

  14. What makes a graph a function? • Each ____________________ is mapped to only one ___________ ______________. • We create a “________________” to see if a ________________ (set of ordered pairs) is a ________.

  15. Domain & Range • Domain: all x-values • List in braces from least to greatest and do not repeat values • Range: all y-values • List in braces from least to greatest and do not repeat values

  16. Domain & Range Example {(3, 4), (-2, 7), (9, 10), (9, 11)} Domain ____________________ Range _____________________

  17. Mapping Diagram NOT A FUNCTION: FUNCTION: (4, 5), (4, -3), (-1, 2), (6,0) (4, 5), (-2, 7), (3, 7), (0, -1) Try using the vertical line test…does the relation pass?

  18. Make a Table, Mapping, & Graph {(9, 2), (-3, 4), (1, 5), (-1, 2)} Table Mapping Graph

  19. Types of Functions • Linear • Quadratic • Absolute Value • Exponential • Cubic

  20. Let’s GRAPH! • Create a T-Chart

  21. Graphing Continued: • Pick values for _____. • Plug in x and use _______ to solve for __. • Plot ordered ______. • Connect the _________. • Include ________ at the end of your line. • _________ your work 

  22. Try these linear functions: • y = 3x + 1 • y = -2x + 3 • y = x – 4 What patterns do you see between the equations and the graph?

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