Unit 1 A
What is a continuous graph?
A graph that has no holes/skips or an asymptote.
What's an inverse?
An inverse is an operation that undoes the operation of a function. The opposite operation.
Describe the shifts that are occurring in this transformation.
- (x+7)3 - 12
The original was x3. It was flipped, moved seven units to the left and 12 units down.
Where do these two equation intersect?
y = 3x + 1 and y = x - 3
They intersect at (-2,-5).
Given the following
f(x) = x4 - 7x3 + 12x2 - 14x
g(x) = 5x3 - 8x2 + 5
h(x) = x3 + 2x - 12
k(x) =x4 + 15
What is h(x) + k(x)?
x4 + x3 + 2x + 3
What's the inverse of 3x + 3?
(x-3)/3
What's the inverse of the point ( 12, 15)?
(15, 12)
Convert from log to exponential form: log11161051=5
115=161,051
Solve for x:
logx (1/2401) = -4
7
Given the following
f(x) = x4 - 7x3 + 12x2 - 14x
g(x) = 5x3 - 8x2 + 5
h(x) = x3 + 2x - 12
k(x) =x4 + 15
What is k(x) - g(x)?
x4 -5x3 + 8x2 + 10
Given the domain and range of f(x) is
Domain : (-12, 7)
Range : (-15,23)
What's the domain and range of the inverse of f(x)?
Domain : (-15,23)
Range : (-12, 7)
What is the difference between an interval of increase, an interval of decrease, and a constant?
Intervals of increase is the range where the function is increasing.
Interval of decrease is the range where the function is decreasing.
The constant is when there is no increase or decrease in the function ( there is no change).
Compress the following logs
log15 7 + log15 x - log15 2 + log15 y
log15 (7x/2y)
Expand the following log
log (8x7/15y)
log 8 + log x7 - log y + log 15
Given the following
f(x) = x4 - 7x3 + 12x2 - 14x
g(x) = 5x3 - 8x2 + 5
h(x) = x3 + 2x - 12
k(x) =x4 + 15
What is f(x) + h(x)?
x4 - 6x3 + 12x2 - 12x -12
What's the inverse of
(3x - 12) / 2
(2x + 12) /3
What's the inverse of
3 + (2 + x)1/2
x2 -6x +7
Solve
1512x+40 = 50,625
log15 50,625 = 12x+40
4 = 12x+40
-36 = 12x
-3 = x
What’s the equation that models the amount of money in an account with a 12% annual interest rate, compounded twice a week, with an initial investment of $ 2,350?
A=2350(1+.12/104)104t
Given the following
f(x) = x4 - 7x3 + 12x2 - 14x
g(x) = 5x3 - 8x2 + 5
h(x) = x3 + 2x - 12
k(x) =x4 + 15
What is f(x) - g(x)?
x4 - 12x3 + 20x2 - 14x -5
Solve for x:
43x+4 = 8x-12
43x+4 = 8x-12
22(3x+4) =23(x-12)
2(3x+4) = 3(x-12)
6x+8 = 3x -36
3x = -44
x = -44/3
Simplify (9-5) x (272)
Leave your answer in exponential form with only positive exponents.
32(-5) * 33(2)
3-10 * 36
3-10+6
3-4
1/34
A new bacteria multiples at a rate of 12.456 per hour. Assuming you have one of these bacteria. How many bacteria will after 10 hours?
Formula made from given information: Given 1(12.456)t
1(12.456)10 = 89,905,445,128
After 10 hours there will be 89,905,445,128 bacteria.
How much money would be in a bank account after 13 and a half years? If the initial amount was $150,000 and it is compounded every other week at a 7% interest rate.
The account would have around $385,432.26.
Given the following
f(x) = x4 - 7x3 + 12x2 - 14x
g(x) = 5x3 - 8x2 + 5
h(x) = x3 + 2x - 12
k(x) =x4 + 15
What is f(x) + h(x) + k(x)?
2x4 - 6x3 + 12x2 - 12x + 3