Sequences
A sequence has a starting value of 2 and a common difference of 3. Write an equation.
an=2+3(n-1)
Which of the following are exponential?
1. a gallon of water drains from a pool each minute
2. half of your ice cream melts every minute
3. a cars value depreciates 30% each year
4. a car drives at a constant speed of 50 miles per hour
2. half of your ice cream melts every minute
3. a cars value depreciates 30% each year
What is another word for average rate of change?
Slope
Which is not a function?
1. {(2,4),(3,6),(6,6)}
2. {(2,4),(3,6),(2,6)}
3. {(2,4),(3,6),(2,4)}
4, {(2,4),(3,4),(6,4)}
2. {(2,4),(3,6),(2,6)}
Solve using your graphing calculator
|3-2x|=5
x=4
Consider the sequence 17, 14, 11, 8, ...
Determine if it is arithmetic or geometric and write an explicit formula.
Arithmetic
an=17-3(n-1)
As x increases beyond 10, which function will have the largest value?
1. g(x)=2.3x
2. g(x)=2.3x2
3. g(x)=2.3x3
4. g(x)=2.3x
4. g(x)=2.3x
Calculate the average rate of change over the interval 1<x<3.
(0,10),(1,11),(2,12),(3,13)
1
Maddie is walking home from the museum. She starts 38 blocks from home and walks 2 blocks per minute. Maddie's distance from home is given by the function D(t) in terms of the number of minutes, t, she has been walking.
D(t) = -2t+38
What is D(5)?
Which domain would be appropriate for a function that predicts the cost, c(s), in terms of the number of shirts, s, purchased?
1. {..., -2, -1, 0, 1, 2, ...}
2. {0, 1.50, 2.45, 6.39, ...}
3. {0, 1, 2, 3, 4, 5, ...}
4. {..., -1, -0.5, 0, 0.5, 1, ...}
3. {0, 1, 2, 3, 4, 5, ...}
Consider the sequence 3, 12, 48, 192, ...
Determine if it is arithmetic or geometric and write an explicit formula.
Geometric
an=3(4)n-1
Joe bought a car for $8750. The cars value depreciates by 12% each year. What is the value of the car after 4 years?
$5247.33
Calculate the average rate of change over the interval [0,2].
(0,10),(1,11),(2,12),(3,13)
1
Maddie is walking home from the museum. She starts 38 blocks from home and walks 2 blocks per minute. Maddie's distance from home is given by the function D(t) in terms of the number of minutes, t, she has been walking.
D(t) = -2t+38
What is t when D(t)=18?
t=10 minutes
What is the vertex of the parabola 2x2+5
(0,5)
Arithmetic Sequence: The 3rd term is 13 and the 5th term is 19. Which is the correct equation?
1. an= 7 + 3n
2. an= 4 + 3n
3. an= 7.4(1.2)n
2. an= 4 + 3n
You open an account with $2500 and an interest rate of 6.5% compounded yearly. How much is in the account after 7 years?
$3884.94
Calculate the average rate of change over the interval [1,7].
(1,16),(4,22),(7,28),(10,34),(13,40)
2
Is the following relation a function? Why or why not?
{(3,1),(6,8),(3,4),(2,6)}
No because x=3 repeats and has 2 different y-values
State the domain and range of the function represented by the set
{(0,1), (2,4), (-3, 7), (-1,-2), (5,-1)}
Domain: {-3, -1, 0, 2, 5}
Range: {-2, -1, 1, 4, 7}
Geometric Sequence: The 3rd term is 12 and the 5th term is 48. Which is the correct equation?
1. an=3(2)n
2. an=1.5(2)n
3. an=3(2)n-1
3. an=3(2)n-1
Mr. Smith invested $250 in a savings account that earns 3% interest compounded annually. He made no additional deposits or withdrawals. Determine the number of dollars in the account at the end of 4 years.
$281.38
Calculate the average rate of change over the interval [0,2].
g(x) = 3x + 8
3
Is the following relation a function? Why or why not?
{(3,2), (4,6), (5,6), (3,2)}
Yes, the only x-value that repeats is x=3, but it is mapped to the same y-value.
How does the graph of
g(x)= -2|x-4|
compare to the graph of
f(x)= |x|?
g(x) translates f(x) right 4, reflects it over the x-axis, and stretches it vertically (shrinks/skinnier)