PREC11 Unit6 notes

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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This document was uploaded on 02/16/2014 for the course MATH Pre-Calcul at Holy Cross Regional High School.

Ask a homework question - tutors are online