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Shifting a Function’s Graph

Dive into the world of function transformations with Lesson 5.1, where we explore the function f(x) = 0.1(x³ - 9x²) using a graphing calculator. Throughout the lesson, you will set parameters to visualize shifts in the graph based on various transformations. Predict the behavior of shifted functions like y1, y2, and y3, and check your predictions against the actual results. Learn how to combine multiple transformations and understand their effects on the graph's position. Engage with exercises to solidify your understanding of shifting functions.

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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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