1. Precalculus Mr. Ueland 2 nd Period Rm 156

2. Today in Precalculus Announcements/Prayer New material – 1.5B: “Stretching and Shrinking Graphs” Continue to work on A15

3. Reflections - Review Vertical reflections mirror the graph across the x-axis, i.e. y = ‒f(x). Horizontal reflections mirror the graph across the y-axis, i.e. y = f(‒x). Are the following graphs vertical or horizontal reflections? Horizontal Vertical

4. Reflections (cont.) There are three graphs on the plot below. Is the small-dash graph a vert. or hort. reflection of the large-dash? What is the function? [see pg 102-3] What relationship does the solid line graph have to the function? It is a translation. f(x) = ln (x) + 2 Vertical f(x) = ln (x)

5. Finding equations for transformations Translations: Reflections: y=(x+2) 2 is two units LEFT y=(x+2) 2 +3 is three units UP negate all terms input (‒x) for every x

6. Vertical and Horizontal Stretching and Shrinking Graphical stretching in the vertical is easy to visualize. Note the following function (what is it?): f(x)=sin (x)

7. Vertical and Horizontal Stretching and Shrinking Stretching this function vertically just multiplies every value of f(x) by a constant: What is the new (red) function? f(x) = 2 sin (x)

8. Vertical and Horizontal Stretching and Shrinking As you would now guess, stretching in the horizontal involves operating on the argument rather than the function itself: Note: the function stretches as the argument shrinks

9. Vertical and Horizontal Stretches, Shrinks Vertical stretches and shrinks are caused by a multiplier c such that Horizontal stretches and shrinks are caused by a multiplier c such that Note: it is 1/c, not c!

10. Example 5 Let C 1 be the curve defined by. Find the equations for the following non-rigid transformations of C 1 : a)C 2 is a vertical stretch of C 1 by a factor of 3. y2y2

11. Ex. 5 (cont.) b)C 3 is a horizontal stretch of C 1 by a factor of 1/2. y3y3 so, we substitute 2x everywhere you see x in f(x)

12. Assignment 15 Read: Section 1.5, pp 131-139 Do: pp139-141/1-23 odd, 25-28, 31, 43, 46- 48, 51-52, 59-64 (28 problems) Due: Friday at the start of class