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NOTE MATH FORM 3 - 13b graf intro

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The document contains examples of graphing various functions including linear, quadratic, and cubic functions. Tables are provided showing the inputs and outputs for each function, and graphs are drawn with the functions plotted. Instructions are given on how to represent different functions using hand gestures. An example problem asks the reader to graph the function y=4x^2-2x-6 and find corresponding x and y-values from the graph.

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Friday, January 25, 2013 Graph of Functions EN.AIRIL BIN AHMAD AIRIL AHMAD
1 Friday, January 25, 2013 −6 −4 −2 2 4 x 6 −1 −2 Graph −3 −4 Functions y= x+ 3 y = x3 + 4 y = 2x2 -5 AIRIL AHMAD
Friday, January 25, 2013 Example 1: Given the function, y = x + 3. Copy and complete the table. Draw a graph based on the data with 2cm to 1 unit on x-axis and 1cm to 1unit on y-axis. X -4 -3 -2 -1 0 1 2 3 4 Y -1 0 1 2 3 4 5 6 7 When x= - 4 : y= - 4 + 3 = -1 When x= 0 : y= 0 +3 = 3 When x= -3 : y= -3 + 3 = 0 When x= 1 : y= 1 +3 = 4 When x= -2 : y= -2 + 3 = 1 When x= 2 : y= 2 +3 = 5 When x= -1 : y= -1 + 3 = 2 When x= 3 : y= 3 +3 = 6 When x= 4 : y= 4 +3 = 7 AIRIL AHMAD
Friday, January 25, 2013 2cm AIRIL AHMAD
Friday, January 25, 2013 2cm AIRIL AHMAD
Friday, January 25, 2013 Y 1cm to 1unit on y-axis 2cm to 1 unit on x-axis X 0 -2 -1 1 2 AIRIL AHMAD
Friday, January 25, 2013 Y 1cm to 1unit on y-axis 2 1 X 0 -2 -1 -1 1 2 AIRIL AHMAD
Friday, January 25, 2013 Example 1: Given the function, y = x + 3. Copy and complete the table. Draw a graph based on the data with 2cm to 1 unit on x-axis and 1cm to 1unit on y-axis. X -4 -3 -2 -1 0 1 2 3 4 Y -1 0 1 2 3 4 5 6 7 When x= - 4 : y= - 4 + 3 = -1 When x= 0 : y= 0 +3 = 3 When x= -3 : y= -3 + 3 = 0 When x= 1 : y= 1 +3 = 4 When x= -2 : y= -2 + 3 = 1 When x= 2 : y= 2 +3 = 5 When x= -1 : y= -1 + 3 = 2 When x= 3 : y= 3 +3 = 6 When x= 4 : y= 4 +3 = 7 AIRIL AHMAD
Friday, January 25, 2013 Y X -2 -1 Y 1 2 2 + 3 = x 1 y X 0 -2 -1 -1 1 2 AIRIL AHMAD
Friday, January 25, 2013 Example 2: Given the function, y = 2x + 1. Copy and complete the table. Draw a graph based on 2cm to 1 unit on x-axis and 1cm to 1unit on y-axis. X -4 -3 -2 -1 0 1 2 3 4 Y -7 -5 -3 -1 1 3 5 7 9 When x=-4 : y= 2x(-4) + 1 = When x= 0 : y= 2x(0) + 1 = 1 -7 When x= 1 : y= 2x(1) + 1 = 3 When x=-3 : y= 2x(-3) + 1 = -5 When x= 2 : y= 2x(2) + 1 = 5 When x=-2 : y= 2x(-2) + 1 = -3 When x= 3 : y= 2x(3) + 1 = 7 When x=-1 : y= 2x(-1) + 1 = -1 When x= 4 : y= 2x(4) + 1 = 9 AIRIL AHMAD
−3 Friday, January 25, 2013 −4 Red Equation : y=x+3 Blue Equation : y=2x+1 AIRIL AHMAD
Friday, January 25, 2013 Example 3: Given the function, y = -4x - 2. Copy and complete the table. Draw a graph based on the data with 2cm to 1 unit on x-axis and 1cm to 2 units on y-axis. X -4 -3 -2 -1 0 1 2 3 4 Y 14 10 6 2 -2 -6 -10 -14 -18 Example 4: Given the function, y = -2x + 2. Copy and complete the table. Draw a graph based on the data with 2cm to 1 unit on x-axis and 1cm to 2 units on y-axis. X -4 -3 -2 -1 0 1 2 3 4 Y AIRIL AHMAD
−4 Friday, January 25, 2013 Red equations : y= -4x-2 Blue equations: y= -2x+4 AIRIL AHMAD
Friday, January 25, 2013 AIRIL AHMAD
Friday, January 25, 2013 Example 5: Given the function, y = x2 - 4. Copy and complete the table. Draw a graph based on the data with 2cm to 1 unit on x-axis and 1cm to 2 units on y-axis. X -4 -3 -2 -1 0 1 2 3 4 Y 12 5 0 -3 -4 -3 0 5 12 Example 6: Given the function, y = 12 -x2 . Copy and complete the table. Draw a graph based on the data with 2cm to 1 unit on x-axis and 1cm to 2units on y-axis. X -4 -3 -2 -1 0 1 2 3 4 Y -4 3 8 11 12 11 8 3 -4 AIRIL AHMAD
Friday, January 25, 2013 AIRIL AHMAD
−2 Friday, January 25, 2013 −4 Red Equation : y= x²+2 Blue Equation : y= 6-x² AIRIL AHMAD
Friday, January 25, 2013 Example 7: Given the function, y = x3 - 2. Copy and complete the table. Draw a graph based on the data with 2cm to 1 unit on x-axis and 2cm to 5 units on y-axis. X -3 -2 -1 0 1 2 3 Y Example 8: Given the function, y = 10 –x3 . Copy and complete the table. Draw a graph based on the data with 2cm to 1 unit on x-axis and 2 cm to 5 units on y-axis. X -3 -2 -1 0 1 2 3 Y AIRIL AHMAD
−4 −3 −2 −1 1 2 3 4 Friday, January 25, 2013 Red Equation : y= x³+2 Blue Equation : y= 10 - x³ AIRIL AHMAD
Friday, January 25, 2013 Use your finger to represent: Y=x Y=-x Y= x2 Y= -x2 Y= x3 Y= -x3 AIRIL AHMAD
Friday, January 25, 2013 Example 9: Given the function, y = 4x2-2x-6. Copy the table and draw a graph based on the data with 2cm to 1 unit on x-axis and 2cm to 5 units on y-axis. X -3 -2 -1 0 1 2 3 Y 38 14 0 -6 -4 6 24 From the graph, find the value of y when: a. X= 2 b. x= 2.2 c. x= -2.5 d. x= -1.5 From the graph, find the value of x when: e. y= 10 f. y= 20 g. y= -5 h. Y = 15 AIRIL AHMAD
Friday, January 25, 2013 AIRIL AHMAD

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NOTE MATH FORM 3 - 13b graf intro

  • 1. Friday, January 25, 2013 Graph of Functions EN.AIRIL BIN AHMAD AIRIL AHMAD
  • 2. 1 Friday, January 25, 2013 −6 −4 −2 2 4 x 6 −1 −2 Graph −3 −4 Functions y= x+ 3 y = x3 + 4 y = 2x2 -5 AIRIL AHMAD
  • 3. Friday, January 25, 2013 Example 1: Given the function, y = x + 3. Copy and complete the table. Draw a graph based on the data with 2cm to 1 unit on x-axis and 1cm to 1unit on y-axis. X -4 -3 -2 -1 0 1 2 3 4 Y -1 0 1 2 3 4 5 6 7 When x= - 4 : y= - 4 + 3 = -1 When x= 0 : y= 0 +3 = 3 When x= -3 : y= -3 + 3 = 0 When x= 1 : y= 1 +3 = 4 When x= -2 : y= -2 + 3 = 1 When x= 2 : y= 2 +3 = 5 When x= -1 : y= -1 + 3 = 2 When x= 3 : y= 3 +3 = 6 When x= 4 : y= 4 +3 = 7 AIRIL AHMAD
  • 4. Friday, January 25, 2013 2cm AIRIL AHMAD
  • 5. Friday, January 25, 2013 2cm AIRIL AHMAD
  • 6. Friday, January 25, 2013 Y 1cm to 1unit on y-axis 2cm to 1 unit on x-axis X 0 -2 -1 1 2 AIRIL AHMAD
  • 7. Friday, January 25, 2013 Y 1cm to 1unit on y-axis 2 1 X 0 -2 -1 -1 1 2 AIRIL AHMAD
  • 8. Friday, January 25, 2013 Example 1: Given the function, y = x + 3. Copy and complete the table. Draw a graph based on the data with 2cm to 1 unit on x-axis and 1cm to 1unit on y-axis. X -4 -3 -2 -1 0 1 2 3 4 Y -1 0 1 2 3 4 5 6 7 When x= - 4 : y= - 4 + 3 = -1 When x= 0 : y= 0 +3 = 3 When x= -3 : y= -3 + 3 = 0 When x= 1 : y= 1 +3 = 4 When x= -2 : y= -2 + 3 = 1 When x= 2 : y= 2 +3 = 5 When x= -1 : y= -1 + 3 = 2 When x= 3 : y= 3 +3 = 6 When x= 4 : y= 4 +3 = 7 AIRIL AHMAD
  • 9. Friday, January 25, 2013 Y X -2 -1 Y 1 2 2 + 3 = x 1 y X 0 -2 -1 -1 1 2 AIRIL AHMAD
  • 10. Friday, January 25, 2013 Example 2: Given the function, y = 2x + 1. Copy and complete the table. Draw a graph based on 2cm to 1 unit on x-axis and 1cm to 1unit on y-axis. X -4 -3 -2 -1 0 1 2 3 4 Y -7 -5 -3 -1 1 3 5 7 9 When x=-4 : y= 2x(-4) + 1 = When x= 0 : y= 2x(0) + 1 = 1 -7 When x= 1 : y= 2x(1) + 1 = 3 When x=-3 : y= 2x(-3) + 1 = -5 When x= 2 : y= 2x(2) + 1 = 5 When x=-2 : y= 2x(-2) + 1 = -3 When x= 3 : y= 2x(3) + 1 = 7 When x=-1 : y= 2x(-1) + 1 = -1 When x= 4 : y= 2x(4) + 1 = 9 AIRIL AHMAD
  • 11. −3 Friday, January 25, 2013 −4 Red Equation : y=x+3 Blue Equation : y=2x+1 AIRIL AHMAD
  • 12. Friday, January 25, 2013 Example 3: Given the function, y = -4x - 2. Copy and complete the table. Draw a graph based on the data with 2cm to 1 unit on x-axis and 1cm to 2 units on y-axis. X -4 -3 -2 -1 0 1 2 3 4 Y 14 10 6 2 -2 -6 -10 -14 -18 Example 4: Given the function, y = -2x + 2. Copy and complete the table. Draw a graph based on the data with 2cm to 1 unit on x-axis and 1cm to 2 units on y-axis. X -4 -3 -2 -1 0 1 2 3 4 Y AIRIL AHMAD
  • 13. −4 Friday, January 25, 2013 Red equations : y= -4x-2 Blue equations: y= -2x+4 AIRIL AHMAD
  • 14. Friday, January 25, 2013 AIRIL AHMAD
  • 15. Friday, January 25, 2013 Example 5: Given the function, y = x2 - 4. Copy and complete the table. Draw a graph based on the data with 2cm to 1 unit on x-axis and 1cm to 2 units on y-axis. X -4 -3 -2 -1 0 1 2 3 4 Y 12 5 0 -3 -4 -3 0 5 12 Example 6: Given the function, y = 12 -x2 . Copy and complete the table. Draw a graph based on the data with 2cm to 1 unit on x-axis and 1cm to 2units on y-axis. X -4 -3 -2 -1 0 1 2 3 4 Y -4 3 8 11 12 11 8 3 -4 AIRIL AHMAD
  • 16. Friday, January 25, 2013 AIRIL AHMAD
  • 17. −2 Friday, January 25, 2013 −4 Red Equation : y= x²+2 Blue Equation : y= 6-x² AIRIL AHMAD
  • 18. Friday, January 25, 2013 Example 7: Given the function, y = x3 - 2. Copy and complete the table. Draw a graph based on the data with 2cm to 1 unit on x-axis and 2cm to 5 units on y-axis. X -3 -2 -1 0 1 2 3 Y Example 8: Given the function, y = 10 –x3 . Copy and complete the table. Draw a graph based on the data with 2cm to 1 unit on x-axis and 2 cm to 5 units on y-axis. X -3 -2 -1 0 1 2 3 Y AIRIL AHMAD
  • 19. −4 −3 −2 −1 1 2 3 4 Friday, January 25, 2013 Red Equation : y= x³+2 Blue Equation : y= 10 - x³ AIRIL AHMAD
  • 20. Friday, January 25, 2013 Use your finger to represent: Y=x Y=-x Y= x2 Y= -x2 Y= x3 Y= -x3 AIRIL AHMAD
  • 21. Friday, January 25, 2013 Example 9: Given the function, y = 4x2-2x-6. Copy the table and draw a graph based on the data with 2cm to 1 unit on x-axis and 2cm to 5 units on y-axis. X -3 -2 -1 0 1 2 3 Y 38 14 0 -6 -4 6 24 From the graph, find the value of y when: a. X= 2 b. x= 2.2 c. x= -2.5 d. x= -1.5 From the graph, find the value of x when: e. y= 10 f. y= 20 g. y= -5 h. Y = 15 AIRIL AHMAD
  • 22. Friday, January 25, 2013 AIRIL AHMAD