The document discusses functions, their domains and ranges, function notation, evaluating functions, and sequences. It provides examples of arithmetic and geometric sequences and how they can be defined using equations. It also discusses determining whether numbers are in the domain of a function and finding the domain and range of functions given their equations or graphs.

1. Functions
Evaluating
Domain and Range
Sequences

2. Function Notation: f(x)
_ is the
input
f is the This does
name of NOT mean
the function f ____ x
f(x)

3. Function Notation: f(x)
x is the
input
f is the This does
name of NOT mean
the function f ____ x
f(x)

4. Function Notation: f(x)
x is the
input
f is the This does
name of NOT mean
the function f times x
f(x)

5. Evaluating functions

6. Domain
If a function is undefined for any
input, we say that number is not in
the domain of the function.

7. What is the domain and range of
this function?
y = 2x + 1

8. What is the domain and range of
this function?
Scatter plot

9. What is the domain and range of
this function?
y = sin x

10. Sequences
Domain = Set of Natural numbers

11. Sequences
Usually some kind of pattern…

12. 5, 10, 15, 20, …
What comes next?

13. 5, 10, 15, 20, 25
This is called an arithmetic
sequence.
“Arithmetic” sequences add the same
number every time to the previous
number.

14. 5, 10, 15, 20, 25
We can define this sequence with an
equation:
f(xn) = xn-1 + 5

15. Can you write an
arithmetic sequence that
starts with -2 and adds 3
each time?

16. 2, 4, 8, 16, …
What comes next?

17. 2, 4, 8, 16, 32
This is called a geometric sequence.
“Geometric” sequences multiply the
same number to the one before.

18. 2, 4, 8, 16, 32
We can define this sequence with an
equation:
f(xn) = 2(xn-1)

19. Can you write a
geometric sequence that
starts with ¼ and
multiplies by 2 each
time?