Lesson 2 1

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Lesson 2 1

  1. 1. 2.1 Represent Relations and Functions<br />A relation is a mapping, or pairing, of input values with output values.<br />Domain – the set of input values.<br />Range – the set of output values.<br />
  2. 2. 2.1 Represent Relations and Functions<br />
  3. 3. 2.1 Represent Relations and Functions<br />Example 1<br />Consider the relation given by (3, 2), (-1, 0), (2, -1), (-2, 1), (0, 3)<br />Identify the domain and range.<br />Represent the relation using a graph and a mapping diagram.<br />
  4. 4. 2.1 Represent Relations and Functions<br />A Function is a relation for which each input has exactly one output. If any input has more than one output the relation is not a function.<br />A function is always a relation.<br />A relation is not always a function.<br />
  5. 5. 2.1 Represent Relations and Functions<br />Example 2<br />ANIMATION<br />
  6. 6. 2.1 Represent Relations and Functions<br />
  7. 7. 2.1 Represent Relations and Functions<br />
  8. 8. 2.1 Represent Relations and Functions<br />
  9. 9. 2.1 Represent Relations and Functions<br />Many functions can be described as a function with two variables.<br />Example: y = 3x – 5<br />The input variable is x, also known as independent variable.<br />The output variable is y, also known as dependent variable.<br />The output depends on the input.<br />An ordered pair is a solution of an equation in two vairables.<br />A graph is another way to represent the solutions of the equation.<br />
  10. 10. 2.1 Represent Relations and Functions<br />
  11. 11. 2.1 Represent Relations and Functions<br />Example 4<br />Graph the equation y = 3x – 5.<br />What is the minimum number of points you need?<br />Where does the graph cross the y-axis?<br />
  12. 12. 2.1 Represent Relations and Functions<br />A function that can be written in the form y = mx + b where m and b are constants is called a linear function.<br />When y is replaced by f(x) the function is written using function notation.<br />y = mx + b  Linear function in x-y notation<br />f(x) = mx + b Linear function in function notation.<br />The notation f(x) is read “the value of f at x” or “f of x” and identifies x as the independent variable.<br />
  13. 13. 2.1 Represent Relations and Functions<br />Example 5<br />Tell whether the function is linear. Then evaluate the function when x = -3. What is the domain & range?<br />f(x) = -2x3 + 5<br />g(x) = 12 – 8x<br />
  14. 14. 2.1 Represent Relations and Functions<br />Graph y = 3x - 2<br />
  15. 15. 2.1 Represent Relations and Functions<br />
  16. 16. 2.1 Represent Relations and Functions<br />In real life, you may need to restrict domain so that it is reasonable to the given situation.<br />To do this inequalities are used.<br />
  17. 17. 2.1 Represent Relations and Functions<br />Example 6<br />The length L (in inches) that a spring stretches when a weight up to 20 pounds is attached to it is given by L(w) = 1/12w + 2, where w is the weight in pounds. Graph the function and determine a reasonable domain and range. What is the length of the spring when a 10 pound weight is attached?<br />
  18. 18. 2.1 Represent Relations and Functions<br />In 1960, the deep sea vessel Trieste descended to an estimated depth of 35,800 feet. Determine a reasonable domain and range of the function P(d) for this trip. P(d) = 1 + 0.03d<br />
  19. 19. 2.1 Represent Relations and Functions<br />How do you graph relations and functions?<br />
  20. 20. 2.1 Extension<br />
  21. 21. 2.1 Extension<br />Example 1<br />Graph y = -x + 3 for x ≥ -1. Classify the function as discrete or continuous. Identify the range.<br />
  22. 22. 2.1 Extension<br />Example 2<br />Mrs. Malone buys paint for $20 per gallon. The function f(x) gives the cost of buying x gallons of paint. Write and graph the function described. Determine the domain and range. Then tell whether the function is discrete or continuous.<br />
  23. 23. 2.1 Extension<br />How do the graphs of discrete functions and continuous functions differ?<br />

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