SECT 2.6EXPONENTIAL FUNCTIONS
© Copyright all rights reserved to Homework depot: www.BCMath.ca
Many events in the real world behave like anexponential function
Anything that grows or decay at a fixed percentage
Examples of how Exponential Functions occur in thereal world include:
Finances – mortgages, investments, life insurancepolicies, compound interest
Nature – Population growth, EarthquakeMagnitudes (Ritcher Scale), Sound intensities
Science – Acidic levels, Carbon dating, BacteriaGrowth
© Copyright all rights reserved to Homework depot: www.BCMath.ca
I) EXPONENTIAL FUNCTION:
x
y
x
y
Domain:
Range:
© Copyright all rights reserved to Homework depot: www.BCMath.ca
II) GRAPHS OF EXPONENTIAL FUNCTIONS
x
y
-5
-4
-3
-2
-1
0
1
2
-1
1
2
3
4
5
6
7
8
9
10
11
12
IF “B” is bigger, the graph willgo up faster!!
© Copyright all rights reserved to Homework depot: www.BCMath.ca
x
y
5
4
3
2
1
0
-1
-2
-1
1
2
3
4
5
6
7
8
9
10
11
12
IF “B” is smaller, the graph willgo down faster!!
© Copyright all rights reserved to Homework depot: www.BCMath.ca
SUMMARY:
For Bases larger than 1
When the base is larger, the graph will increase faster
For Bases between 0 and 1
When the base is smaller, the graph will decrease faster
Note: If there are no vertical shifts in the graph, thenthe x-axis will be a horizontal asymptote
© Copyright all rights reserved to Homework depot: www.BCMath.ca
EX: GIVEN THE EQUATIONS, INDICATE WHICHOF THE FOLLOWING IS THE CORRECT GRAPH
3
5
6
4
© Copyright all rights reserved to Homework depot: www.BCMath.ca
III) GRAPHING EXPONENTIAL FUNCTIONS WITHTRANSFORMATIONS
Use the functions tool kit to graph exponential functions withtransformations (Ch 1)
Ex: Indicate the transformations and graph the function:
V.C. by a factor of ½
H.S. of 3 units right
V.S. of 2 units up
© Copyright all rights reserved to Homework depot: www.BCMath.ca
PRACTICE: INDICATE THE TRANSFORMATIONS FOREACH OF THE FOLLOWING EQUATIONS:
H.S. 1 unit right
V.E. by a factor of 3
H.C. by a factor of ½
V.C. by a factor of 2/3
V.S. 6 units up
H.C. by a factor of 1/3
V.E. by a factor of 3/2
V.S. 5 down
H.S. 2 left
© Copyright all rights reserved to Homework depot: www.BCMath.ca
PRACTICE: INDICATE THE TRANSFORMATIONSFOR EACH OF THE FOLLOWING EQUATIONS:
Note:
Rewrite the equation in the form:
HorizontalReflection
Note:
Rewrite the equation in the form:
HorizontalExpansion by 2
© Copyright all rights reserved to Homework depot: www.BCMath.ca
EXPONENTIAL FUNCTIONS WITH A CHANGE OF BASE:
You can change the base of a function by adding aextra exponent
The function will stay the same, but just have adifferent base
The equation can now
be written differently as:
Base is changed to 2
Constant of “k” is added
to the exponent
Solve for the exponent
© Copyright all rights reserved to Homework depot: www.BCMath.ca
PRACTICE: EXPRESS THE FOLLOWING AS A BASE 3FUNCTION:
The equation can now
be written differently as:
© Copyright all rights reserved to Homework depot: www.BCMath.ca
HOMEWORK:
© Copyright all rights reserved to Homework depot: www.BCMath.ca