January 03, 2018

DO NOW!

2) Sit quietly in your seat so that we can start class quickly. Consider which problems you have questions about from last night's HW.

1) Take out last night's homework assignment and raise your hand for a stamp.

January 03, 2018

Today's Agenda:1) 9.2 HW questions

2) 9.3: Graphing General Rational Functions

3) 9.3 (Ext I): Oblique/Slant Asymptotes

January 03, 2018

Questions from last night's homework?

January 03, 2018

9 Steps to Graphing a Rational Function:1.) Factor if necessary; Determine domain.2.) Find holes. Plot them. 3.) Find vertical asymptotes; draw them.4.) Find the y-intercept. Find the x-intercept(s). Plot Both.5.) Find the horizontal asymptote if it exists. Draw it. Identify range.6.) Find the oblique/slant asymptote if it exists. Draw it.7.) Divide the graph into intervals using the x intercepts

and vertical asymptotes. Plug in a value from each interval. Plot those points.

8.) Determine the behavior near each asymptote.9.) Put it all together to finish the graph.

January 03, 2018

Investigating a Rational Function:• With your table, complete investigation #2

Domain:

Range:

V.A.:

X-int:

Y-int:

H.A.:

January 03, 2018

9.3: Date:

• I CAN graph general rational functions

Use Graph Paper

January 03, 2018

Example: Putting it all together

Domain?

Holes?

Vertical Asymptotes?

x-intercepts?

y-intercept?

Horizontal Asymptote?

Interval:

January 03, 2018

Example: Putting it all together

Domain?

Holes?

Vertical Asymptotes?

x-intercepts?

y-intercept?

Horizontal Asymptote?

Interval:

January 03, 2018

Your chance to learn more about your classmates!

Who is __________?We will ask question until the timer ends. Be creative!

Ground Rules:- Inappropriate questions will end the activity. Act responsibly so we can all enjoy the opportunity to get to know each other!

VIPSpotlight

January 03, 2018

9 Steps to Graphing a Rational Function:1.) Factor if necessary; Determine domain.2.) Find holes. Plot them. 3.) Find vertical asymptotes; draw them.4.) Find the y-intercept. Find the x-intercept(s). Plot Both.5.) Find the horizontal asymptote if it exists. Draw it. Identify range.6.) Find the oblique/slant asymptote if it exists. Draw it.7.) Divide the graph into intervals using the x intercepts

and vertical asymptotes. Plug in a value from each interval. Plot those points.

8.) Determine the behavior near each asymptote.9.) Put it all together to finish the graph.

January 03, 2018

Are there other types of asymptotes?Of Course!

Horizontal & Oblique AsymptotesWe will look at 4 possible scenarios:

1) degree of numerator < degree of denominator

2) degree of numerator = degree of denominator

3) degree of numerator is 1 higher than the degree of denominator

4) degree of numerator is 2+ higher than the degree of denominator

January 03, 2018

9.3 (Ext I): Date:

• I CAN find oblique (slant) asymptotes

Use Graph Paper

January 03, 2018

3) degree of numerator is 1 higher than the degree of denominator

January 03, 2018

4) degree of numerator is 2+ higher than the degree of denominator

January 03, 2018

H.A.: end behavior vs. non-end behavior

January 03, 2018

Concept Check:

Today we learned....

1) How to graph general rational functions

Tonight's Homework:

9.3 Worksheet Answer keys on class website!

9.3 (Ext. I) Worksheet

Assigned: __________ Stamped: _________ Due: __________

January 03, 2018

Homework Time!• You may work alone or with the other members of

your table• Use your time Productively!