Warm-Up• Solve:

• Solve: =5

• Solve:

Homework Questions

Rational Functions Day 2With Limits

Infinite Limits - Asymptotes•

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Infinite Limits - Asymptotes•

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Infinite Limits - Asymptotes•

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Algebraically…using limits• Anytime you are given an equation – factor first!• Take the limit at all points of discontinuity!

• If you get then you have a hole at that point…• You will have to find the (x,y) coordinate of the hole!

• If you get then you have a VA at that x-value…• You will have to do limits to talk about behavior and be able to

graph without a calculator!

Finding Holes using limits• •

Finding VA using limits•

Finding VA using limits•

61)( 2

xxxxf

Find VA and holes using limits•

422)( 2

2

xxxf

Long Division•

Long Division

1133)(

23

x

xxxxf

Long Division

Homework• P. 246 • (11-18)• (19-22) State all VA and holes using limits• (37, 40, 41, 44) you need to find VA and holes using limits, state

domain and range, increasing/decreasing intervals.