Composite Functions
If f(x) = 5x - 3 and g(x) = x2 + 12x.
Find (f - g)(x)
-x2 - 7x - 3
Inverse means ________.
Opposite
When you multiply by the same variable, you ___ the exponents.
Add
How do we know if an exponential function is exponential growth?
The number connected to the exponent has to be bigger than 1.
Michael invests $1000 in an account with 5% interest. How much will he have if the money compounds quarterly for 2 years?
$1477.45
If f(x) = 5x - 3 and g(x) = x2 + 12x.
Find (g * x)(x)
5x3 + 57x2 - 36x
Find the inverse of the relation (0, -1) ( 2, 3) (5, -6)
(-1, 0) (3, 2) (-6, 5)
When you divide by the same variable, you ___ the exponents.
Subtract
How do we know if an exponential function is exponential decay?
The number connected to the exponent has to be smaller than 1.
Michael invests $1000 in an account with 5% interest. How much will he have if the money compounds semi-annually for 2 years?
$1215.50
If h(x) = x3 - 10 and m(x) = -2x + 4
Find (h o m)(6)
-522
Find the inverse of the function y = x + 7
x - 7 = y
True/False
Your final answer can have a negative exponent in it.
False
Identify the y-int and if the function is growth or decay.
y = 3(0.35)x
y-int = 3, decay
What are the values for monthly, daily, and weekly?
Monthly = 12
Daily = 365
Weekly = 52
If h(x) = x3 - 10 and m(x) = -2x + 4
Find (m o h)(-3)
78
Find the inverse of f(x) = -6 + 2x
(x + 6)/2 = y
(2x3 y-4 )(-5x2 y)
(-10x5 )/(y3)
A school has 100 seniors this year. The student body increases by 6% each year. How much seniors will the school have in 2 years?
112
Michael invests $1000 in an account with 5% interest. How much will he have if the money compounds continuously for 2 years?
$1105.17
A large pizza costs $25.00. If the 1st coupon is $5.00 off and the 2nd coupon is half off, how much is the pizza?
$10.00
What is the symbol for inverse of f(x)?
f-1(x)
Simplify (-8)2/3
4
You bought a car for $15,000. The car depreciates at 5.5%. How much will the car be worth after 8 years?
$9539.94
Michael invests $1000 in an account with 5% interest. How many years will it take him to double his money?
15 years