Arithmetic Sequences
Define "arithmetic sequence"
An order of numbers defined by a constant increasing or decreasing pattern.
Define "function"
A relation where every input has exactly one output
Which axis is vertical and which axis is horizontal?
y-axis is vertical and x-axis is horizontal
Define the "slope" of a graph
change in y / change in x
rise over run
how much the dependent variable changes divided by how much the independent variables changes
The T-Mobile family plan has a one-time activation fee of $80 and costs $160 per month. If you make a graph showing the cost of the family plan over a certain number of months, what is the slope of the line and what does it represent?
$160 cost per month
Define "common difference"
How much a sequence is increasing or decreasing by between terms. It is a constant number between each term.
What are all of the terms used to describe the x-variable and the y-variable?
y-variable: output, dependent variable, range
Define "y-intercept"
The point where a graph crosses the y-axis
(4, 9) and (8, 11) are two points on a graph. What is the slope of the graph?
(11 - 9) / (8 - 4) = 2/4 = 1/2
The T-Mobile family plan has a one-time activation fee of $80 and costs $160 per month. If you make a graph showing the cost of the family plan over a certain number of months, what would be the y-intercept?
(0, 80) or the starting cost/activation fee
Consider the sequence: 30, 22, 14, 6, -2, -10...
What is a4?
a4 = 4th term = 6
Consider the function f(x) = 3x + 4
Give a pair of input and output in the form (x,y)
Examples: (0, 4), (1, 7), (2, 10), (3, 13), ...
How can you tell if a graph is a function?
Use the vertical line test: if a vertical line can pass through the graph at more than 1 point it means there is an input with more than 1 output so it is not a function.
What is the slope between the two points on the graph?
(2-6) / (3-1) = -4 / 2 = -2
You saved $300 to spend on vacation. You budget to spend $25 each day. Write a function to represent how much money you will have left after any day of vacation.
V(d) = 300 - 25d
Consider the sequence: 11, 24, 37, 50, 63, ...
What would be the explicit formula to find any term of this sequence?
an = 11 + 13(n-1)
What is the minimum of the graph?
(4, -3)
What is the formula to find the rate of change between two points on a graph?
(y2 - y1) / (x2 - x1)
If a graph is decreasing, why will it have a negative slope?
Because the change in y will be decreasing so the rise will be a negative number.
You saved $300 to spend on vacation. You budget to spend $25 each day. If you graph the amount of money left remaining after each day of vacation, what would your slope represent?
-25, spending $25 each day
Gloria is saving up to buy a car. So far she has $500 in her savings account. She decides to add $200 to her account every month.
How much money will she have in her account after 7 months?
Use explicit formula: an = a1 + d(n-1)
a7 = 500 + 200(6) = $1700
Where is the graph constant?
x < 2 and x > 8
You make $9 per hour at work. You want to make a graph of how much your check will increase as you work more hours. What variable would your y-axis represent?
y-axis is the dependent variable, which is the amount of money you will make - because the amount of money depends on the amount of hours.
Sarah's parents give her a $100 allowance each month. She likes to spend her allowance on comic books. She made a graph showing how much of her allowance she spends on comic books.
What does the slope between the points (0, 100) and (1, 95) represent?
When Sarah buys 0 comic books, she still has $100. When she buys 1 comic books she has $95 left. So each comic book costs $5 from her allowance.
You saved $300 to spend on vacation. You budget to spend $25 each day. If you graph how much money you have remaining after each day of vacation, what would your y-intercept represent?
(0, 300) or the amount of money saved up before leaving for vacation