Transformations of Functions
What are the different kinds of transformations?
shift, stretch, compress, or flip
What is the product rule? Explain or draw an example
Combine the logs and multiply the arguments/ values
Ex: Logx+Logy=Log (xy)
Convert the log into exponential form:
Logac=b
ab=C
A=Pert
Identify the type of transformation: f(x) + d
Vertical Translation
What is the power rule?
nlogx=logxn
Convert into exponential form:
Log525=2
52=25
What do the parts in the continuous compound formula stand for?
A= Final Amount
P= Principal
r= Rate
t=Time
Identify the two types of transformations in this expression: -f(x+3)
Reflection across the x-axis, Horizontal shift: left 3
Identify the log rules for rewriting the expression into a single log:
2Log3(x)+Log3(x^3)
Power rule
Product Rule
Solve for m
Log3(27)=m
m=3
Dash invested $10,000 at 3% interest compounded continuously. How much will he have after 8 years?
A=$12712.4915
List the transformations in the equation:
f(x)= 3(x-4)2+10
-Vertical Stretch by 3
-Horizontal Shift: Right 4
-Vertical Shift: Up 10
Write the expression as a single logarithm:
Log4(x)-Log4(x3)
Log4(1/x2)
Solve for w.
Log41+Log4(w+24)=4
w=232
Ashleigh wants to double her money. She put $5,000 in a bank account that pays 4% compounded continuously. How long will it take her to double her money? (Round to the nearest tenth.)
t= 17.3 Years
List the transformation and the equation's domain and range:
f(x)= Log4 (x-6)+7
-Vertical Shift: 7 up
-Domain: x>6
-Range: All Real Numbers
Write the expression as a single logarithm:
3Log(x)+2Log(x)
Log(x)5
Solve for n.
Log4(n+7) + Log4(6)=4
n=35.667
Lily invested $400 in an account earning 4.5% interest, compounded continuously. How long will it take her to triple the value of her money?
24.41 years