Topic 5 Review
(3a)^-3
1/27a^3
Interstate Park the deer population was estimated to be 2000 and increasing continuously at a rate of 4% per year. If you increase continues at this rate what is expected deer population in 10 years?
2,983
write an expression for f(g(x)) given f(x)=5x and g(x)=4x+14 what about f(f/x)
20x+70 25x
Multiply (fg)(x) when f(x)=2√x and g(x)=√x, then find the domain.
2x neg infinity to pos infinity
g(x)=7x, h(x)=5x-12. Write an expression for g(h(x)).
35x-84
if f(x)=6x+4, what is f(f(x))?
36x+28
y=4.7(1.65)^x Initial Amount Growth or Decay Rate of growth or decay
4.7 growth 65%
y=5000(0.85)^x Initial amont growth or decay rate of growth or decay
5000 decay -15% or -.15
f(g(7)) if f(x)=x+1 and g(x)=x^2+4
54
f(x)=x+4 and g(x)=5x-7 Write a function for f(x)+g(x) Write a function for f(x)-g(x) what is the domain of each?
6x-3 4x-11 -infinity to pos infinity
(2x^2y^-2z^3/2)(3x^-3y^3z^-1)
6yradical z ------------- x
verticle line test
Vertical lines drawn through the graph May intersect the graph one and only one time each in order for the relation to be a function
what type of regression would be used on a arch
a quadratic regression
what does e stand for
an irrational constant
Continue is different than...
compounding
what is a function?
every x value has 1 y value
find the inverse f(x)=6x+4
f^-1 (x)=1/6x-2/3 f^-1(x)=x-4/6
what is g(f(x)) if f(x)=2x and g(x)=x+10
g(2x)=2x+10
find the inverse g(x)=x-4/7
g^-1(x)=7x+4
horizontal line test
horizontal lines drawn through the graph May intersect the graph one and only one time each in order for the function to be a one-to-one function
inverse means to
switch the x and the y
Divide (f/g)(x) when f(x)=x^3 and g(x)=x^2, then find the domain?
x neg infinity to pos infinity
x^n+4 times x^n+7
x^2n+11
find the inverse y=2x-6
y=1/2x+3
is h(x)=x-5 a one to one function? how about f(s)=s^2
yes no
Say you win the lottery and get $1000000. Each month you spent 10% of your money. How much of the money will you have at the end of the year?
$282,429.54
Sarah has $12,500 to invest in a long-term savings account. The Bank she chooses offers 2.25% interest rate compounded monthly. How much will Sarah make in interest after 10 years?
$3150.74
Suppose you have saved $10,000 after graduation. You plan on leaving the money in an account that earns an interest rate of 1.25%. The bank compounds the interest each month. How much money will you earn after 4 years?
$512.44
what is (fg)(-2) if f(x)=x+4 and g(x)=2x-3?
-14
given the function g(x)=.6^x, what is the percent change over intervals of 1 unit?
-40%
Suppose the annual interest rate at a bank is 4%. We can write the function f(t)= 1.04^t to describe this. How can we calculate the equivalent monthly rate?
.327%
The annual interest rate of a mutual fund is 4%. What is the approximate quarterly rate (that is, the rate paid every 3 months)?
.985%
The element fermium has a Decay constant of -0.00866 per day. After 41 days, how much fermium will remain of a 10.0 gram sample round to the nearest whole gram.
7 grams
Consider the exponential function f(x)=4 x 2^x. What is the average rate of change between 1 and 2?
8
One to One functions
A relation is a one-to-one function if their relation itself and its inverse are both functions each x gets one y and vise versa
What is the Continueous growth or decay formula?
A=A\/0e^rt A=Pe^rt
What is the formula for compound interest?
A=P(1+r/n)^nt
Composite function
One function being applied to the results of another function. Made up of two functions, taking me out for the first function and using it as an input to the second function.
Conversion Formulas
T=M/12 M=12T T=Q/4 Q=4T
