Download presentation

Presentation is loading. Please wait.

Published byCora Grimwood Modified over 2 years ago

1
1 Example 7 Sketch the graph of the function Solution I. Intercepts The x-intercepts occur when the numerator of r(x) is zero i.e. when x=0. The y-intercept occurs at r(0)=0. II. Asymptotes Vertical asymptotes occur where the denominator of r(x) is zero, i.e at x=1. The horizontal asymptote on the right is given by: The horizontal asymptote on the left is given by: Thus r has the x-axis as a horizontal asymptote on both the left and the right.

2
2 III. First Derivative By the quotient rule, the derivative of is: The denominator of r / (x) is always positive so the sign of r / (x) is determined by the sign of its numerator 1+2x. Hence r / (x) is positive for –1/2

3
3 IV. Vertical Tangents and Cusps r has a vertical tangent at x=0 because both the left and right derivatives have value + . V. Concavity and Inflection Points By the quotient rule, the derivative of is: Then r // (x)>0 for A 1 and r is concave down there. We depict this information on a number line.

4
4 Since the concavity of r changes from down to up at x=A and x=B, the function r has an inflection point there. Since the concavity of r changes from up to down at x=0, the function r has an inflection point there. Note that x=1 is not an inflection point because r has a vertical asymptote at x=1 and x=1 is not in the domain of r. VI. Sketch of the graph We summarize our conclusions and sketch the graph of r.

5
5 x-intercepts: x=0 y-intercept: y=0 vertical asymptote: x=1 horizontal asymptote: x-axis on the left and right vertical tangent: y-axis decreasing: x<-1/2 increasing: -1/2

Similar presentations

OK

Rational Functions Objective: To graph rational functions without a calculator using what we have learned.

Rational Functions Objective: To graph rational functions without a calculator using what we have learned.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on schottky diode voltage Convert free pdf to ppt online convert Ppt on regular expression library Full ppt on electron beam machining set Ppt on carbon and its compounds ppt Ppt on 3d geometry maths class 11 Ppt on green revolution and its impact on india Ppt on area of parallelogram and triangles and quadrilaterals Ppt on women empowerment Mems display ppt on tv