Rational functions day 2.pptx worked
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This document appears to be notes from a math class covering topics in rational functions including infinite limits, asymptotes, using limits to find holes and vertical asymptotes, and examples of using long division and limits to solve related problems. It provides instructions for homework involving using limits to find vertical asymptotes and holes in rational functions, stating the domain and range and intervals of increase/decrease.
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Rational functions day 2.pptx worked
- 1. Warm-Up • Solve: log 3𝑥 + 4 = 2 • Solve: 𝑙𝑜𝑔2(−𝑥 − 4)=5 • Solve: 2 ln 𝑥 − 7 = 9
- 3. Rational Functions Day 2 With Limits
- 4. Infinite Limits - Asymptotes • •
- 5. Infinite Limits - Asymptotes • •
- 6. Infinite Limits - Asymptotes • •
- 7. Algebraically…using limits • Anytime you are given an equation – factor first! • Take the limit at all points of discontinuity! • If you get 0 0 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!
- 8. Finding Holes using limits • •
- 9. Finding VA using limits •
- 10. Finding VA using limits • 6 1 )( 2 xx x xf
- 11. Find VA and holes using limits • 4 22 )( 2 2 x x xf
- 12. Long Division •
- 14. Long Division
- 15. 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.