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Functions

Learn about functions, domain and range, graphing, f(x) notation, and calculating slope. Practice identifying domain and range, graphing equations, using f(x) notation, and calculating slopes of lines. Includes examples and exercises.

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Functions

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  1. Functions Domain-Range Graphing f(x) Notation Calculating Slope

  2. Domain-Range • The collection of all input values is called the “Domain”. • Most likely will be the x-values. • The collection of all output values is called the “Range”. • Most likely will be the y-values. • A relation is a function if and only if each input corresponds to one output.

  3. Identify the Domain & Range Is the relation a function?

  4. Identify the Domain & Range Is the relation a function?

  5. Identify the Domain & Range Is the relation a function?

  6. y 10 10 8 6 4 2 x -10 -10 -8 -6 -4 -2 2 4 6 8 10 10 -2 -4 -6 -8 -10 -10 Graphing UsingInput-Output Tables • Take each input-value and plug it in. • Plot the point. • Graph the line. 2(0)+1 = 1 5 7

  7. y 10 10 8 6 4 2 x -10 -10 -8 -6 -4 -2 2 4 6 8 10 10 -2 -4 -6 -8 -10 -10 You Try One! 10 4 0 -6

  8. y 10 10 8 6 4 2 x -10 -10 -8 -6 -4 -2 2 4 6 8 10 10 -2 -4 -6 -8 -10 -10 Try Another One! -3 1 5 9

  9. f(x) Notation • Plug in. • Evaluate.

  10. You Try Some!

  11. Calculating Slope Positive Rises • (2, 5) and (-1, -4) • (-6, 7) and (6, 3) • (2, 1) and (4, 1) • (4, 3) and (4, 8) m = 3 Negative Falls m = -1/3 Zero Horizontal m = 0 Undefined Vertical m is undefined

  12. Parallel vs. Perpendicular • Parallel Lines have the same slope different y-intercepts. • Perpendicular lines have opposite-reciprocal slopes.

  13. Tonight’s HW • 2.1 #20-38Even • 2.2 #20-30Even, 32-35, 41-44 • Have fun 

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