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Understanding Functions: Domain, Range, and the Vertical Line Test

This resource covers key concepts of functions, including identifying functions through tables and graphs. It explains how to determine if equations like y = x² or x = |y| are functions, using the Vertical Line Test for graphs. Additionally, it discusses range and domain, including real numbers and restrictions like denominators and square roots. Explore the domain and range of specific equations, and learn valuable skills through example problems and assignments. This guide is essential for mastering foundational function concepts in mathematics.

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Understanding Functions: Domain, Range, and the Vertical Line Test

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  1. 12.2 Functions and Graphs

  2. F(X) = x+4 where the domain is {-2,-1,0,1,2,3}

  3. To determine if an equation is a function… Create a (x, y) table

  4. Is y = x² a function? Is x = y2 a function? No, because x = 9 is equal to both 3 and –3.

  5. YES Is y = |x| a function? Is x = |y| a function? No, because x = 7 is equal to both 7 and –7.

  6. To determine if a graph is a function… Perform the Vertical Line Test

  7. Is this a graph of a function? Vertical Line Test

  8. Is this a graph of a function?

  9. Is this a graph of a function?

  10. Is this a graph of a function?

  11. Is this a graph of a function?

  12. Is this a graph of a function?

  13. Domain of a Function • X values have to make the value a real number • Watch for 0 in the denominator • Watch for – under the square root (set radicand )

  14. Find the domain of Domain is {x | x  4}

  15. Find the domain of Domain is {x | x  -5}

  16. Find the domain of Domain is all real numbers

  17. Find the domain of Domain is {x | x  4}

  18. Find the domain of Domain is {x | x  7}

  19. Graph and State Domain and Range • Domain is horizontal coverage • Range is vertical coverage

  20. Find the domain of f(x) = 2x + 1 Domain is all real numbers

  21. Find the range of f(x) = 2x + 1 Range is all real numbers

  22. Find the range of Range is { y | y  0 }

  23. Find the range of Range is { y | y  -1 }

  24. AssignmentPage 545(2-10 even and 11-31all)

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