Arithmetic Sequences
What is the explicit formula?
an=a1+d(n-1)
Evaluate f(x) = 3x + 4 for x = 5
f(5)=19
Domain is all the possible ____ values. List at least 3 terms for the blank.
Independent Variable
x
Input
n
A movie ticket costs $10. Write a function to represent this situation.
c(t)=10t
What distinguishes linear functions from quadratic functions?
Straight line vs curve/U/parabola
Determine the common difference of the sequence: 12, 15, 18...
+3
If h(x) = 5x - 2, what is h(0)?
h(0)=-2
Write a complete sentence of what this would sound like if you read it out loud. R: [0, 20).
A Sun Flower grows 3 inches per month. If it is currently 12 inches tall, represent its height in function notation.
h(m)=3m+12
What does the slope of a linear function represent in an arithmetic sequence?
Common Difference
Find the 10th term of the sequence: 5, 8, 11, …
32
g(2)=-6
{y|3<y<5} represent the _____, which is all possible _____ values.
There is only one correct answer for the first blank. List at least 2 correct answers for the second blank.
1: range
2: Output, dependent variable, y, f(x), an
If a car travels at a speed of 60 mph. This can be represented by the function d(t)=60t. What does d(2)=120 mean in context?
In 2 hours, the car travels 120 miles.
An open circle on a graph would mean you ____ that value. In interval notation you represent this by using a ____ and in set notation you use ___ or ___.
exclude
( curved parenthesis )
< or > not with the or equal to line.
Write the first five terms of the arithmetic sequence with the initial term of 7 and a common difference of -3.
7, 4, 1, -2, -5
Image should be a straight line that goes through the point (5,2) in this direction /
Which parent graphs have domain of all real numbers and a range of all positive numbers including 0.
Absolute value AND quadratic.
If a person earns $20 per hour, what is the independent and dependent variables?
Independent: Hours
Dependent: Money earned
Write this in interval notation. {x|3≤x<500} {y|y∈ℝ}
D: [3,500)
R: (-∞, ∞)
What is the difference between the explicit and recursive formulas? (Do not just read them, analyze and explain the difference)
The explicit formula requires both the initial term and common difference. It can be used to find any term in a sequence. While the recursive formula only uses the common difference, but can only find the next term in a sequence.
Hudson was offered a job after college earning a salary of $35,000. He will get a raise of $4,000 each year.
Write a function to represent this situation.
Evaluate your function for m(8).
Explain what m(8) means in context.
m(y)=4000y+35000
m(8)=67000
After working at the company for 8 years, he will earn $67,000.
Write a complete sentence of what this would sound like if you read it out loud. {x|x>5, x∈ℕ}
The set of x, such that x is greater than 5, belongings to natural numbers.
A store sells t-shirts for $15 each. Desribe the domain of this situation.
[0, ∞)
{x|x≥0, x∊ℕ}
You can only sell whole numbers of t-shirts. It needs to be positive and it needs to be a non-fraction.
Write an arithmetic sequence where the initial term is how long Mr. Fritsche has been teaching and the common difference is how many cats he has.
6, 10, 14...
an=6+4(n-1)
Or put it in a table