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1.4 Shifting, Reflecting, and Sketching Graphs

1.4 Shifting, Reflecting, and Sketching Graphs. Students will recognize graphs of common functions such as: Students will use vertical and horizontal shifts and reflections to graph functions. Students will use nonrigid transformations to graph functions. Vertical and Horizontal Shifts.

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1.4 Shifting, Reflecting, and Sketching Graphs

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  1. 1.4 Shifting, Reflecting, and Sketching Graphs • Students will recognize graphs of common functions such as: • Students will use vertical and horizontal shifts and reflections to graph functions. • Students will use nonrigid transformations to graph functions.

  2. Vertical and Horizontal Shifts Experiment with the following functions to determine how minor changes in the function alter the graphs:

  3. Student Example If , make a guess and check with the calculator. Give the function that would move f(x): • down 4 units • left 3 units • right 2 units and up 5 units

  4. Vertical and Horizontal Shifts Let c be a positive real number. Vertical and horizontal shifts in the graph of y=f(x) are represented as follows: 1. Vertical shift c units upwards: h(x)=f(x)+c Ex.Moves up 2 units from 2. Vertical shift c units downward: h(x)=f(x)-c Ex. Moves down 2 units from 3. Horizontal shift c units to the right: h(x)=f(x-c) Ex. Moves right 2 units from 4. Horizontal shift c units to the left: h(x)=f(x+c) Ex. Moves left 2 units from

  5. Example 1: Compare the graphs of each function with the graph of

  6. Example 2 The graph of is shown in Figure 1.44. Each of the graphs in Figure 1.45 is a transformation of the graph of f. Find an equation for each function. y=g(x) y=h(x)

  7. Student Example:What must be done to the point (x,y) to reflect over the x-axis and the y-axis. y • (x,y). • x

  8. Reflections in the Coordinate Axes Reflections in the coordinate axes of the graph of y = f(x) are represented as follows. • Reflection in the x – axis: h(x) = -f(x) • Reflection in the y – axis: h(x) = f(-x)

  9. Student Example • Find an equation that will: • reflect f(x) over the x-axis. • Reflect f(x) over the y-axis.

  10. Example 3 The graph of is shown. Each graph shown is a transformation of the graph of f. Find an equation for each function. f(x) y=g(x) y=h(x)

  11. Example 4 Compare the graph of each function with the graph of a. b. c.

  12. Example 5: Nonrigid Transformations Compare the graph of each function with the graph of a. b.

  13. Example 6 Compare the graph of with the graph of

  14. Tuition has risen at private colleges. The table lists the average tuition for selected years. Use a non-rigid transformation of a linear function to best fit the data: Use the function to predict the cost of tuition during your freshmen year of college. Does it seem accurate?

  15. Use a non-rigid transformation to adjust a quadratic to best fit the data: Use the function to predict the number of AIDS fatalities in 2010.

  16. p.48-50#3-63x3

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