Assignment, pencil red pen, highlighter, GP notebook, graphing calculator U4D7 Have out: Bellwork: Graph each function on the same set of axes. Be sure to identify the inflection point. 2 4 6 8 10 y x –2 –4 –6 –8 –10 f(x) = (x + 4)3 – 2 f(x) = (x + 4)3 – 2 inflection point: (–4, –2) +1 +3 +3 inflection point: (5, 3) +1 total:

Asymptote Recall: Asymptote: Example: PG – 77 Asymptote Recall: Asymptote: A line that is a close approximation to a particular curve as the curve goes off to infinity in one direction. The curve becomes very, very close to the asymptote line, but never touches it. vertical asymptote x = – 3 2 4 –2 –4 6 8 –6 –8 x y Example: horizontal asymptote y = 0

Done Yesterday we grouped the following equations: cubic reciprocal exponential Done Today we will look at reciprocal functions. Be sure to have a graphing calculator.

Reciprocal Locator point (0, 0) Group name: _______________ Functions (parent graph) (0, 0) Equation: _____ locator point: _____ x = 0 x y -4 -0.25 -3 -0.33 -2 -0.5 -1 ERR 1 2 0.5 3 0.33 4 0.25 x y -4 -3 -2 -1 1 2 3 4 2 4 6 8 10 y x –2 –4 –6 –8 –10 Locator point (0, 0) y = 0 Link to Geo Sketch

(h, k) (0, –4) Equation: ________ locator point: _____ x = 0 x y -4 -4.25 -3 -4.33 -2 -4.5 -1 -5 ERR 1 2 -3.5 3 -3.67 4 -3.75 x y -4 -3 -2 -1 1 2 3 4 2 4 6 8 10 y x –2 –4 –6 –8 –10 Locator point (0, -4) y = -4 Link to Geo Sketch

(h, k) (3, 0) Equation: ________ locator point: _____ x y -2 -0.2 -1 -0.25 -0.33 1 -0.5 2 3 ERR 4 5 0.5 6 0.33 x y -2 -1 1 2 3 4 5 6 2 4 6 8 10 y x –2 –4 –6 –8 –10 x = 3 Locator point (3, 0) y = 0 Link to Geo Sketch

(h, k) x = –3 (–3, 1) Equation: ________ locator point: _____ x y -4 -3 -2 -1 1 2 3 4 x y -4 -3 ERR -2 2 -1 1.5 1.33 1 1.25 1.2 3 1.166 4 1.429 2 4 6 8 10 y x –2 –4 –6 –8 –10 Locator point (–3, 1) y = 1 Link to Geo Sketch

PARENT GRAPH TOOLKIT x y -3 -2 -1 1 2 3 x y Name: Reciprocal 10 x y -3 -2 -1 1 2 3 x y Name: Reciprocal 8 Parent Equation: 6 4 Description of Locator: 2 (1, 1) y = 0 (0, 0) x intersection of asymptotes (h, k) –4 –2 2 4 (–1, –1) –2 General Equation: –4 –6 –8 Properties: –10 x = 0 vertical asymptote Domain: Range: x = h {x| x  h} {y| y  k} horizontal asymptote y = k

Based on the patterns you have observed, graph the next 4 reciprocal functions on the worksheet WITHOUT using a graphing calculator. 2 4 6 8 10 y x –2 –4 –6 –8 –10

Finish today's assignment: PG 69-73 & worksheets