Vocabulary words

Arithmetic sequence- A sequence of numbers such that

the difference between the consecutive terms is constant.  Example- 3,5,7,9,11,13 cd=2

Geometric sequence- A sequence of numbers where each

term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

Example - 1,3,9,27,81 cr= 3

Explicit formula-A formula that allows direct computation

of any term for a sequence a1, a2, a3, 

Example- An= A1+ (n-1) d

Horizontal shift/vertical shift- Horizontally translating

a graph is equivalent to shifting the base graph left or right in the direction of the x-axis. A vertical shift is when the graph literally moves vertically, up or down. The movement is all based on what happens 

An example of a function -

(-3,5), (-2, 5), (-1, 5), (0, 5), (1, 5), (2, 5)

Domain - {-3, -2, -1, 0, 1, 2}

Range - 5

An example of no function -

(2, -3), (4, 6), (3, -1), (6, 6), (2, 3)

Domain - {2, 3, 4, 6}

Range - {-3, -1, 3, 6}

Helen wants to lose weight so she has a plan to exercise for 20 minutes and wants to double it every month. But the problem is she has never in her life exercised but she hopes to stick to her plan. The exponential function using function notation would be h(x)= 15. 2^n-1. Based on the scenario, the number of the month is going to be x. We want to know how many minutes can Helen exercise by the 12th month.

h(x)= (20)2^n-1

h(12)= (20)2^12-1

h(12)= (20)2^11

h(12)= (20)2,048

h(12)= (20)^40,960

By us plugging in the 12 into the function, Helen now knows that she will be exercising 40,960 minutes in the 12th month. It will be hard for her but she has faith in herself and knows she can do it.

Recursive Formula - t1=50 tn= (tn-1)2.

Wishes Mobile cellular phone service charges $0.30 for each minute the phone is being used. The linear function would be y= 0.30x and the function notation that would model this linear function would be f (x)= 0.30x. For us to show how this function might be evaluated for inputs in the domain based on the context of the scenario, you could ask how much it would cost if you used the phone for 20 minutes. You would plug in 20 for x and your answer would be 6. f(20)=0.30(20) f(20)6 it will cost 6 dollars if you use your phone for 20 minutes.

Interpreting linear and exponential functions

One day Mary Sue went to the supermarket and remembered that her best friends birthday was coming up. She knew she had to be a great friend and get her something and knew she had a good taste in music. She saw a gift card for music on iTunes. She got a $100 gift card and her friend started buying $1 songs with it. What is the relationship between the number of songs she buys and how much is going to be left on the card?

Equation= y=-x+100

Intercepts

x=(100,0)

y=(0,100)

Intervals

0,1,2,3,4,5,6,7,8,9,10 all the way too 100

increasing or decreasing

0>99=increasing 0<99=decreasing

End behaviors

x,+infinity x,-infinity

Analyzing Linear and Exponential Functions

Linear function: f(x)=2x+1

Exponential Function: f(x)=2^x

Linear function algebraically: f(x)=2x+1

Linear function verbal description: Macie has a graph. The graph represents the ratio from apples to oranges. For every single apple there are two oranges. She thinks that the linear function that represents this situation is f(x)=2x+1. Is she correct? (the correct answer is yes)

Building functions

How to find:

Explicit expression: the pattern of the first term multiplied by the common ratio raised to a power of one less than the term number.

Recursive expression: stating the first term, and the. Stating the formula to be the common ratio times the previous term.

Sequence: 

5,10,20,40,60 

Recursive: Ax2

Explicit: a(n+1)x5

1. L:-2x+y=9 

2. L: 6x-3y=5 

3. E: g(x)=2x+4

4. E: f(x)=2x

Vertical translations: A translation of a geometric object in a direction parallel to the vertical axis of the Cartesian coordinate system

.

Ex1. h(x)=(x+2)2

Ex2. F(x)=x2

Ex3. G(x)=(x-3)2

A man named Jeremy owns a zoo, each year the amount of lions in the zoo doubled. his first year of taking care of the zoo, there were only 2 lions. Jeremy also had to pay for food for the lions in the zoo which is 100 dollars a month or 1200 dollars in a year.

sequence for amount of lions: 2,4,8,16,32

sequence for amount of money payed for food per year: 1200, 2400, 3600, 4800, 6000

The constant rate of change is +100 per month or +1200 per year because that is the amount of money it costs to buy food for the lions. The constant percent rate is x2 because the amount of lions going up every year doubles. To the right is the graph for the amount of money is costs to buy the food per year.