Section 7.4 Reciprocal Functions

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Presentation transcript:

Section 7.4 Reciprocal Functions i) Concept of Reciprocal Functions ii) Asymptotes, Invariant Points, iii) Graphing the Reciprocal of Linear and QF iv) Domain and Range © Copyright all rights reserved to Homework depot: www.BCMath.ca

I) What is a Reciprocal ? A reciprocal is a number you get when switching the value of the numerator (Top) with the denominator (Bottom). Ex: Find the reciprocal of each number: Notice that the reciprocal of 1 and – 1 will stay the same The reciprocal of 0 is undefined The reciprocal any value between 1 and – 1 will become larger The reciprocal any value larger than 1 will be smaller © Copyright all rights reserved to Homework depot: www.BCMath.ca

II) The Reciprocal of a Function? When finding the reciprocal of a function, put the function in the denominator and place a “1” above it Note: Taking the reciprocal of a number will not change the sign Ie: The reciprocal of a positive number is positive ie: The reciprocal of a negative number stays negative © Copyright all rights reserved to Homework depot: www.BCMath.ca

iii) Graphing Reciprocal Functions The reciprocal function takes the reciprocal of all the y-coordinates of a function When graphing a reciprocal function, there are a three main steps: The reciprocal of 1 or -1 will be the same, so points with a y-coordinate of 1 will not change The reciprocal of zero is undefined, so points with a y-coordinate of zero will become a vertical asymptote Take the reciprocal of all y-coordinates to find where the points of the new function is. Reciprocal of large numbers become small Reciprocal of small numbers become large © Copyright All Rights Reserved Homework Depot www.BCMath.ca

Ex#1) Graph y = 0.5x+1 1. First graph the line: 4. Take the reciprocal of the Y coordinate for every point y = 0.5x+1 2. Find X-intercept (when y = 0)  Vertical Asymptotes 3. Find Common Points: Points where the Y-coordinate is 1 or -1 © Copyright all rights reserved to Homework depot: www.BCMath.ca

Practice: Given the following graph, draw the reciprocal function x y -5 5 Find the x-intercept  Vertical Asymptote Find common points with a Y-coordinate of 1 or -1 Pick some points on the original Function and take the reciprocal of the Y-coordinate Reciprocal of large numbers will become small Reciprocal of small numbers will become large © Copyright All Rights Reserved Homework Depot www.BCMath.ca

Practice: Graph x y -4 -2 2 4 6 8 -6

Practice: Graph the following y Pick some points on the original Function and take the reciprocal of the Y-coordinates. Reciprocal of large numbers will become small Reciprocal of small numbers Will become large Graph 5 Find X-intercept Asymptotes x Find the Common Points where Y coordinate is 1 or -1. -4 4 -5 © Copyright All Rights Reserved Homework Depot www.BCMath.ca

Graph the reciprocal of each parabola x y -5 5 x y -5 5 Use the first x-intercept to draw the Vertical asymptote There are no x-intercepts, so no VA Only one invariant point Plot the invariant points Graph each side of the asymptote © Copyright all rights reserved to Homework depot: www.BCMath.ca

Ex#) Given the following graph f(x), graph the reciprocal function. Find X-intercept Asymptotes Find Common Points Near to Far & Far to Near © Copyright all rights reserved to Homework depot: www.BCMath.ca

Given the following function, indicate the domain and Range: © Copyright all rights reserved to Homework depot: www.BCMath.ca

Practice: Given the following graph f(x), graph the reciprocal function. y -6 -4 -2 2 4 6

Example 7: Given the following graph f(x), graph the reciprocal function. y -8 -6 -4 -2 2 4 6 8

Summary: Reciprocal Function: Graphing Reciprocals Find x-intercepts  Vertical Asymptotes Find common points: where the y-coordinate is 1 or –1 Big  Small Small  Big take the reciprocal of the y-coordinates only Reciprocal and Inverse are not the same!!!

Homework: Assignment 7.4 x y -5 5 5 © Copyright all rights reserved to Homework depot: www.BCMath.ca

Homework: Assignment 7.4 x y -5 5 5 © Copyright all rights reserved to Homework depot: www.BCMath.ca

Homework: Assignment 7.4 x y -5 5 x y -5 5 5 Assignment 7.4 x y -5 5 © Copyright all rights reserved to Homework depot: www.BCMath.ca