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Splash Screen. Ch. 11-2 Functions. Vocabulary:. Function: a relationship where one thing depends upon another. E.g. f(x) = 7x (textbook p.517) f(x) is read as function of x. E.g. f(4) is read as function of 4. Function table: a table that organize the input, rule, and output of a function

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  1. Splash Screen

  2. Ch. 11-2 Functions

  3. Vocabulary: • Function: a relationship where one thing depends upon another. E.g. f(x) = 7x (textbook p.517) • f(x) is read as function of x. E.g. f(4) is read as function of 4. • Function table: a table that organize the input, rule, and output of a function • Domain: the set of input values • Range: the set of output values

  4. For example: f(x) = 4x – 1 is a function. Below is its function table. f(-3) = 4(-3) -1 = -12 – 1 = -13 Domain Range

  5. Find the function value of Example 2-1a Substitute 4 for x into the function rule. Answer:

  6. Find the function value of Example 2-1b Answer: –5

  7. Find the function value of Answer: Example 2-2a Substitute –6 for x into the function rule. Simplify.

  8. Find the function value of Example 2-2b Answer: 2

  9. Complete the function table for Example 2-3a Substitute each value of x, or input, into the function rule. Then simplify to find the output.

  10. Inputx Rule 4x – 1 Output f(x) 0 1 Example 2-3b Answer:

  11. Complete the function table for Example 2-3c Answer:

  12. Answer: The function represents the situation. Example 2-4a PARKING FEESThe price for parking at a city lot is $3.00 plus $2.00 per hour. Write a function using two variables to represent the price of parking for h hours. Words Cost of parking equals $3.00 plus $2.00 per hour. Function

  13. Answer: Example 2-4b TAXIThe price for a taxi ride is $5.00 plus $4.00 per hour. Write a function using two variables to represent the price of riding a taxi for h hours.

  14. Example 2-5a PARKING FEESThe price for parking at a city lot is $3.00 plus $2.00 per hour. How much would it cost to park at the lot for 2 hours? Substitute 2 for h into the function rule. Answer: It will cost $7.00 to park for 2 hours.

  15. Example 2-5b TAXIThe price for a taxi ride is $5.00 plus $1.00 per hour. How much would it cost for a 3 hour taxiride? Answer: $17.00

  16. End of Lesson 2

  17. Lesson 3 Contents Example 1Graph a Function Example 2Use x- and y-intercepts

  18. Graph x x – 3 y (x, y) (0, –3) 0 –3 0 – 3 1 1 – 3 –2 (1, –2) 2 2 – 3 –1 (2, –1) 3 3 – 3 0 (3, 0) Example 3-1a Step 1 Choose some values for x. Make a function table. Include a column of ordered pairs of the form (x, y).

  19. Note that the ordered pair for any point on this line is a solution of The line is the complete graph of the function. Answer: y = x – 3 (3, 0) (2, –1) (1, –2) (0, –3) Example 3-1b Step 2 Graph each ordered pair. Draw a line that passes through each point.

  20. Example 3-1b Check It appears from the graph that (–1, –4) is also a solution. Check this by substitution. Write the function. Simplify.

  21. Graph Example 3-1c Answer:

  22. MULTIPLE-CHOICE TEST ITEMWhich graph represents A B C D Example 3-2a

  23. Read the Test Item You need to decide which of the four graphs represents The graph will cross the x-axis when Example 3-2b Solve the Test Item Replace y with 0. Subtract 1. Simplify. Divide by 2. Simplify.

  24. The graph will cross the y-axis when The x-intercept is and the y-intercept is1. Graph D is the only graph with both of these intercepts. Example 3-2c Replace x with 0. Simplify. Simplify. Answer: D

  25. MULTIPLE-CHOICE TEST ITEMWhich graph represents Example 3-2e Answer: C

  26. End of Lesson 3

  27. Lesson 4 Contents Example 1Positive Slope Example 2Negative Slope Example 3Zero Slope Example 4Undefined Slope

  28. Ch. 11-4 Slope Formula Vocabularies/ concepts: Slope: the ratio of the rise to the run. Slope = rise run m = y2 – y1 x2 – x1 Positive slope: E.g.(3,4) (-1,2)

  29. Ch. 5-1 Slope Negative slope: E.g. (-4,1) (-1,-2) Zero slope: E.g. (-1,2) (1,2) Undefined slope: E.g. (1,3) (1,-2)

  30. Example 4-1a Find the slope of the line that passes through A(3, 3) and B(2, 0). Definition of slope Simplify.

  31. Example 4-1b CheckWhen going from left to right, the graph of the line slants upward. This is consistent with a positive slope. Answer: The slope is 3.

  32. Example 4-1c Find the slope of the line that passes through A(4, 3) and B(1, 0). Answer: 1

  33. Example 4-2a Find the slope of the line that passes through X(–2, 3) and Y(3, 0). Definition of slope Simplify.

  34. Answer: The slope is . Example 4-2b CheckWhen going from left to right, the graph of the line slants downward. This is consistent with a negative slope.

  35. Answer: Example 4-2c Find the slope of the line that passes through X(–3, 3) and Y(1, 0).

  36. Example 4-3a Find the slope of the line that passes through P(6, 5) and Q(2, 5). Definition of slope Simplify.

  37. Example 4-3b Answer: The slope is 0. The slope of any horizontal line is 0.

  38. Example 4-3c Find the slope of the line that passes through P(1, 6) and Q(2, 6). Answer: 0

  39. Example 4-4a Find the slope of the line that passes through G(2, 4) and H(2, 6). Definition of slope Simplify.

  40. Example 4-4b Answer: Division by 0 is not defined. So, the slope is undefined. The slope of any vertical line is undefined.

  41. Example 4-4c Find the slope of the line that passes through G(–2, 1) and H(–2, 0). Answer: undefined

  42. End of Lesson 4

  43. Lesson 5 Contents Example 1Find Slopes and y-intercepts of Graphs Example 2Find Slopes and y-intercepts of Graphs Example 3Graph an Equation Example 4Graph an Equation to Solve Problems Example 5Graph an Equation to Solve Problems Example 6Graph an Equation to Solve Problems

  44. Ch.11-5 Vocabularies/ concepts: Slope-intercept form: y = mx + b So, if y = 2x + 5 What is the slop? What is the y-intercept? Slope y-intercept

  45. Write an equation of the line whose slope is and whose y-intercept is –6. Slope-intercept form Replace m with and b with –6. Answer: Example 3-1a

  46. Ch. 5-3 Slope-intercept Form Vocabularies/ concepts: Slope-intercept form: Y = mx + b So, with one coordinate and the slope, we can write the slope-intercept form and grape it. Slope y-intercept

  47. Answer: Example 3-1b Write an equation of the line whose slope is 4and whose y-intercept is 3.

  48. State the slope and the y-intercept of the graph of the equation of Write the equation in the form Answer: The slope of the graph is and the y-intercept is –5. Example 5-1a

  49. State the slope and the y-intercept of the graph of the equation of Example 5-1b Answer:

  50. State the slope and the y-intercept of the graph of the equation of Write the equation in the form Example 5-2a Write the original equation. Subtract 2x from each side. Simplify. Answer: The slope of the graph is –2 and the y-intercept is 8.

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