1. Precalculus Mr. Ueland 2 nd Period Rm 156

2. Today in PreCalculus Announcements/Prayer Hand in Assn 18 New material: Sec 2.2, “Power Functions with Modeling” Assignment 19

3. Power Functions DEFINTION: A power function is any function that can be written as: If a > 0, then f(x) varies directly with x If a < 0, then f(x) varies inversely with x If a is a positive integer, f(x) is a monomial function

4. Graphing monomials Using you grapher, plot f(x)=x 3 and f(x)=x 5 with [-2.35,2.35] by [-1.5,1.5] Now plot f(x)=x 2 and f(x)=x 4 with [-1.5,1.5] by [-0.5,1.5] So, for f(x)=x n, if n is even, f(x) is even and if n is odd, f(x) is odd. Now plot f(x) = 2x, g(x) = 2x 3 and h(x) = 2x 5. Do these graphs share any ordered pairs? (-1,-2), (0,0), (1,2)

5. Graphing Monomials (cont). There are four general shapes for graphs of the monomial function f(x) = kx a (pg 185) If a = 1, the graph is a line If a > 1, the graph is an “upswinger” (concave up) in the first quadrant If 0 < a < 1, the graph is a “downswinger” (concave down) in the first quadrant If a < 0, the graph is asymptotic If k > 0, the graphs are in Quadrant I If k < 0, the graphs are in Quadrant IV

6. Example 4a Describe the function graph without using your grapher. a.f(x) = 2x –3 The graph is odd (a is odd) The graph is in Quads I/III (k > 0) The graph is asymptotic to both axes (a < 0) The graph passes through (1,2) and (-1,-2) (odd graphs pass through (±1,±k)

7. Example 4b Describe the function graph without using your grapher. b.f(x) = –0.4x 1.5 The graph is undefined for x <0 (to see this, write a as a fraction, 3/2) The graph is in Quad IV (k<0) The graph is a “downswinger” (Quadrant IV, a>1) The graph passes through (1,–0.4) (k=–0.4)

8. Example 4c Describe the function graph without using your grapher. c.f(x) = –x 0.4 Why does this function have a domain, but f(x) = –x 0.41 does not? The graph is even, it is in Quads III/IV, it is an “upswinger” and passes through (±1,–1) Convert a to a fraction: 0.4 = 4/10=2/5 (odd denom.) 0.41 = 41/100 (even denom.)

9. Assignment 19 Read: pp 181-189 Do: pp 189-191/1-23 odd, 29-34, 35-47 eoo, 51,54, 57 (4 pts), 58-63 (31 problems) Due: Tuesday at the start of class

10. Have you regressed? Turn on STAT PLOT 1 Enter lists in EDIT Your grapher will find various regressions (best fit curves) in CALC PwrReg (power regression) is down the list (A on mine) Enter the lists that you want worked with using NAMES (or the L 1 key): PwrReg L 1, L 2