Warm-Up
• Solve: log 3𝑥 + 4 = 2
• Solve: 𝑙𝑜𝑔2 (−𝑥 − 4)=5
• Solve: 2 ln 𝑥 − 7 = 9
Homework Questions
Rational Functions
Day 2
With 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!
0
0
• 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
𝑎 𝑛𝑢𝑚𝑏𝑒𝑟
0
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
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Finding VA using limits
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Finding VA using limits
x 1
• f ( x) 
x2  x  6
Find VA and holes using limits
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2x 2  2
f ( x)  2
x 4
Long Division
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Long Division
x 3  3x 2  3x  1
f ( x) 
x 1
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.
• Sticker WS! Due on review day!