Exercise y answer x 2 x x 2 xr y y 0 yr y 1 by 2x

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Unformatted text preview: nal expression What is the domain of the reciprocal function y = What is the range of the reciprocal function y = 1 ? 2x − 3 1 ? 2x − 3 1 ? 2x − 3 x Unit 6: Day 4 notes - Reciprocal Functions (Part 1) Page 3 of 4 1 ; determine non-permissible values, the domain, and the range 2−x before graphing the function. exercise: y = [Answer: x ≠ 2 ; {x| x ≠ 2, x∈R}; {y| y ≠ 0, y∈R}] y 1 by 2−x transforming the graph of the linear function. exercise: Draw the graph of y = 3 -3 0 3 x 3 x -3 y exercise: Draw the graph of y = 1 by f ( x) transforming the graph of 3 2 if x > 2 f (x) = x if − 2 ≤ x ≤ 2 −2 if x < −2 -3 0 -3 Unit 6: Day 4 notes - Reciprocal Functions (Part 1) GRAPHING y = 1 a ( x − p)2 + q Page 4 of 4 , THE RECIPROCAL OF A QUADRATIC FUNCTION example: Draw the graph of y = 1 . x − 4x + 3 2 y y = x2 − 4x + 3 o Draw the graph of y = (x − 2)2 − 1 It's vertex equation is The vertex is (2,−1) 2 It's factored form is y = (x − 1)(x − 3) The x-intercepts are (1,0) and (3,0) 0 2 4 x -2 o At the points on the quadratic graph with y-coordinate 0, the reciprocal graph will not have a point for that x-value. o At the points on the quadratic graph with y-coordinates approaching 0, the reciprocal graph will have points with y-values going to ∞ or −∞; there are vertical asymptotes at the quadratic function's x-intercepts. o At the points on the quadratic graph with y-coordinates 1 or −1, the reciprocal graph will have the same points; these are invariant points. o At the points on the quadratic graph with y-coordinates going to ∞ or −∞; the reciprocal graph will have points approaching the x-axis; the x-axis is a horizontal asymptote for the left and right ends of the reciprocal graph. exercise: Draw the graph of y = y 1 x −4 2 3 -3 0 -3 3 x PRE-CALCULUS 11 Unit 6 – Day 5: RECIPROCAL FUNCTIONS (Part 2) MODELLING PROBLEMS WITH RECIPROCAL FUNCTIONS There are pairs of quantities that are reciprocals. One well known pair of reciprocal quantities are frequency and period. F...
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This document was uploaded on 02/16/2014 for the course MATH Pre-Calcul at Holy Cross Regional High School.

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