Summary of Lesson (2-4-13) (Ryan)

LESSON 1

Addition of Case 7 and 8

Case 7

y=3e^x

y=-e^x

y=e^0 (This is not exponential)
y=3e^x + 4
y= -e^x -4
y=e^-x

y = | x |

if x>0, y=x
if x<0, y=-x
if x=0, y=0

Case 8

y= 3lgx

y= -lgx (Reflection about the y-axis)

y= lnx

y= 3lgx + 4

y= -lgx - 4

y= log2 x

Case 2a

y= |-3/4x|

or

y=abs (-3/4 x)

y=|3/4x|

or

y=abs (3/4 x)

Hint: For EOY Mr Johari can convert normal graph problems to a trigonometry problem or add in different topics

Let y = f(x)

Case 1: y = -f(x)

this would be a reflection about the x-axis

Case 2: y = f(x) + c

this would be a vertical shift (moving up and down the graph)

Case 3: y = f(-x)

this would be a reflection about the y-axis

case 4: y = absolute f(x)

when x > 0 , y = f(x)

when x < 0 , y = -f(x)


LESSON 2

Prove that

1                              1
_______     +  _________ = 1
log a ab           log b ab

Answer (Courtesy of Justin) :

log a a               log b b
_______     +  _________ =  log ab a (change to base a )+ log ab b = log ab ab = 1
log a ab           log b ab