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LETU MATH 1303 - Shifting a Function’s Graph

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Shifting a Function’s GraphTools for ExplorationShifting the GraphSlide 4Which Way Will You Shift? Which Way Will It Shift? Make It ShiftSlide 8Numerical ResultsAssignmentShifting a Function’s GraphLesson 6.1Tools 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 functionShifting 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 functionsUse different styles for each of the functionsShifting the Graph •How close wereyour predictions?•Try these functions – again, predict resultsy1= 0.1 (x3 - 9x2) y2= y1(x - 2) y3= y1(x) - 2Which Way Will You Shift? 1. f(x) + a 2. f(x - a) 3. f(x)*a 4. f(x + a) 5. f(x) - a A) shift down a units B) shift right a units C) shift left a units D) shift up a units E) turn upside down F) none of these Matching -- match the letter of the list on the right with the function on the left.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) + 5Make 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?Make It Shift•To move the graph down 4 units and left 7 units use the transformationf(x + 7) - 4Numerical Results•Given the functiondefined by a table•Determine the value of the following transformationsx -3 -2 -1 0 1 2 3f(x) 7 4 9 3 12 5 6f(x) + 3 f(x + 1) f(x - 2)Assignment•Lesson .65.1•Page 229•Exercises 1 – 41


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