Tricky log graphs
- 1. Block 3 Tricky log Graphs
- 2. What is to be learned? • How to draw and recognise nasty log graphs
- 3. Previously y = log4x y = 4x y = x y = log4x 1 1
- 4. y = log4x y = log4x 1 (4, 1) ( , 0) x y y = log41 y = 0 y = log44 y = 1 x = 1 x = 4 (1 , 0) (4 , 1) Mini log rules are very helpful
- 5. Draw y = 4 log5x sub x = 1 and x = 5 x=1 y = 4log51 = 4 X 0 (1 , 0) x=5 y =4 log55 = 0 (5 , 4)= 4= 4 X 1 (5, 4) (1, 0) y = 4 log5x
- 6. Draw y = 6 log7x sub x = 1 and x = 7 x=1 y = 6log71 = 6 X 0 (1 , 0) x=7 y =6 log77 = 0 (7 , 6)= 6= 6 X 1 (7, 6) (1, 0) y = 6 log7x
- 7. Draw y = 2 log3(x – 1) sub x = 2 and x = 4 x=2 y = 2log3(2 – 1) = 2 X log31 (2 , 0) x=4 y = 2log3(4 – 1) = 2 X 0 (4 , 2)= 2 X 1 = 2 X log33 (4, 2) (2, 0) y = 2 log3 (x – 1) want to equal 1 and 3 = 0 = 2
- 8. Sketching Nasty Log Graphs Tactics Find 2 points using mini log rules i.e. chose x values to make loga1 and logaa
- 9. Draw y = 5log4(x – 2) sub x = 3 and x = 6 x = 3 y = 5log4(3 – 2) = 5 X log41 (3 , 0) x = 6 y = 5log4(6 – 2) = 5 X 0 (6 , 5)= 5 X 1 = 5 X log44 (6, 5) (3, 0) y = 5 log4 (x – 2) want to equal 1 and 4 = 0 = 5
- 10. Draw y = 6 log3(x + 2) sub x = -1 and x = 1 x=-1 y = 6log3(-1 + 2) = 6 X log31 (-1 , 0) x=1 y = 6log3(1 + 2) = 6 X 0 (1 , 6)= 6 X 1 = 6 X log33 (1, 6) (-1, 0) y = 6 log3 (x + 2) want to equal 1 and 3 = 0 = 6 Key Question
- 11. Identifying Log Graphs (6, 7) (2, 0) Type y = a log5 (x + b) ?
- 12. Identifying Log Graphs (6, 7) (2, 0) Type y = a log5 (x + b) x y x = 2, y = 0 → 0 = a log5 (2 + b) This one first!
- 13. Identifying Log Graphs (6, 7) (2, 0) Type y = a log5 (x + b) x y x = 2, y = 0 → 0 = a log5 (2 + b) must equal 1 b = -1 y = a log5 (x – 1) x y x = 6, y = 7 7 = a log5 (6 – 1)
- 14. Identifying Log Graphs Type y = a log5 (x + b) x = 2, y = 0 → 0 = a log5 (2 + b) must equal 1 b = -1 y = a log5 (x – 1) x = 6, y = 7 7 = a log5 (6 – 1) 7 = a log5 (5) 1 7 = a y = 7 log5 (x – 1)
- 15. Identifying Log Graphs (2, 3) (-1, 0) Type y = a log4 (x + b) x y x = -1, y = 0 → 0 = a log4 (-1 + b)
- 16. Identifying Log Graphs Type y = a log4 (x + b) x = -1, y = 0 → 0 = a log4 (-1 + b) must equal 1 b = 2 y = a log4 (x + 2) x y x = 2, y = 3 3 = a log4(2 + 2) (2, 3) (-1, 0) x y
- 17. Identifying Log Graphs Type y = a log4 (x + b) x = -1, y = 0 → 0 = a log4 (-1 + b) must equal 1 b = 2 y = a log4 (x + 2) x = 2, y = 3 3 = a log4 (2 + 2) 3 = a log4 (4) 1 3 = a y = 3 log4 (x + 2)
- 18. Identifying Log Graphs Type y = a log5 (x + b) Need to find a and b mini log rules are vital again
- 19. This one first! (6, 4) (4, 0) Type y = a log3 (x + b) x y x = 4, y = 0 → 0 = a log3 (4 + b) must equal 1 → b = -3 y = a log3 (x – 3) x y x = 6, y = 4 4 = a log3 (6 – 3) 4 = a log3 3 1
- 20. Type y = a log3 (x + b) x = 4, y = 0 → 0 = a log3 (4 + b) must equal 1 → b = -3 y = a log3 (x – 3) x = 6, y = 4 4 = a log3 (6 – 3) 4 = a log3 3 1 4 = a y = 4 log3 (x – 3) * * * Mini Log Rules
- 21. (6, 2) (2, 0) Type y = a log5 (x + b) x y x = 2, y = 0 → 0 = a log5 (2 + b) must equal 1 → b = -1 y = a log5 (x – 1) x y x = 6, y = 2 2 = a log5 (6 – 1) 2 = a log5 5 1 2 = a y = 2 log5 (x – 1) Key Question
- 22. (12, 15) (5, 0) Type y = a log2 (x + b)Nastier! y = 5 log2 (x – 4) (7, 8) (-1, 0) Type y = a log3 (x + b) y = 4 log3 (x + 2) 1. 2.