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Shifting a Function’s Graph

Shifting a Function’s Graph. Lesson 5.1. Tools for Exploration. Consider the function f(x) = 0.1(x 3 – 9x 2 ) Enter this function into your calculator on the y= screen Set the window to be  -10 < x < 10   and   -20 < y < 20 Graph the function. Shifting the Graph.

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Shifting a Function’s Graph

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  1. Shifting a Function’s Graph Lesson 5.1

  2. Tools for Exploration • Consider the function f(x) = 0.1(x3 – 9x2) • Enter this function into your calculator on the y= screen • Set the window to be  -10 < x < 10   and   -20 < y < 20 • Graph the function

  3. Shifting the Graph • Enter the following function calls of our original function on the y= screen: • y1=  0.1 (x3 - 9x2)  • y2=   y1(x + 2)  • y3=   y1(x) + 2 • Before you graph the other two lines, predict what you think will be the result. Use different styles for each of the functions

  4. Shifting the Graph • How close wereyour predictions? • Try these functions – again, predict results • y1=  0.1 (x3 - 9x2)  • y2=   y1(x - 2)  • y3=   y1(x) - 2

  5. Which Way Will You Shift?  Matching -- match the letter of the list on the right with the function on the left.

  6. Which Way Will It Shift?  • It is possible to combine more than one of the transformations in one function: • What is the result of graphing this transformation of our function, f(x)? f(x - 3) + 5

  7. Make It Shift • It has been moved to the right 3 and up 5 • Now what would you do if you wanted to move the graph down 4 units and left 7 units?

  8. Make It Shift • To move the graph down 4 units and left 7 units use the transformation f(x + 7) - 4

  9. Numerical Results • Given the functiondefined by a table • Determine the value of the following transformations

  10. Assignment • Lesson 5.1 • Page 200 • Exercises 1 – 41 odd

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