What’s a Function?
A function assigns each input to how many outputs?
Exactly one
Arithmetic sequences grow by a constant ___?
Difference
Geometric sequences grow by a constant ___?
Ratio
Saving $10 each week is what type of sequence?
Arithmetic (linear)
what is a function?
A function is like a rule or machine that takes an input, does something to it, and gives back exactly one output.
Is the relation {(1, 2), (2, 3), (1, 4)} a function? Why or why not?
No, because input 1 has two outputs
Write the first 4 terms if a1=3 and d=4
3, 7, 11, 15
Write the first 4 terms if a1 = 2, r=3
2, 6, 18, 54
A cell population doubles every day. What type of sequence?
Geometric (exponential)
Write a function rule for “a number doubled plus 5.”
f(x)=2x+5
Is the relation {(1, 2), (2, 3), (6, 4), (9,4)} a function? Why or why not?
Yes, this relation is a function, because every input has exactly one output.
Explicit formula for 2, 6, 10, 14, …
an = 2+(n−1)(4)
Explicit formula for 5, 10, 20, 40, …
an = 5 x 2n-1
You put $500 in a savings account that earns 5% interest. Is this arithmetic or geometric?
Geometric (growth by multiplying)
Write a recursive formula for the sequence: 12, 15, 18, 21,...
an = an-1 +3
Chase is planning a fundraiser where he sells custom t-shirts. Each t-shirt costs $12 to make, and he plans to buy the machine to make then which cost $50. Write a function that represents Chase’s total amount spent if he plans this fundraiser.
C(x)=12x+50
Graphically, arithmetic sequences look like what type of graph?
Graphically, geometric sequences look like what type of graph?
curved/ exponential
Which type of sequence will eventually grow faster: arithmetic or geometric?
Geometric, because multiplying grows faster than adding
What is the recursive formula for the sequence: 2, 4, 8,... ?
an = 2an-1
A vending machine gives two snacks for $1.50. Is this a function from money → snack?
No, because one input gives two outputs
If the 20th term is 95 and the difference is 5, what’s the first term?
-5
If the 6th term is 243 and r=3, what is the first term?
1
A sequence doubles each time: 1, 2, 4, 8,....
If you graph the points (n,an), will the graph curve upward, form a straight line, or stay flat?
It will curve upward because it’s a geometric (exponential) sequence.
Why are arithmetic and geometric sequences considered functions?
Because each input n maps to exactly one output an