1. A3 7.1a To Identify a Function and to Determine the Domain and Range.
Got ID?
Have your notebook open and be ready to go!

2. Opener: Please copy.
A function is a relation or correspondence that assigns to every element in the domain exactly one element in the range. In other words, if you put a value for x into an equation, you will only get one answer.
The domain is where you get the x’s (questions, independent variable).
The range is where you get the y’s (answers, dependent variable).
When we look at ordered pairs, very simply, the x’s do not repeat. But, it’s OK for the y’s to repeat.

3. Don’t worry about copying this page, just watch:
Let’s look at some ordered pairs: (2, 5) (3, 6) (4, 7)
(5, 7)
(2, 6)
The domain: The range: 2 3 4 5 6 7 5
Undefined!

4. Vertical Line Test: If no vertical line intersects a given graph in more than one point, then the graph is a function. In other words, if any vertical line does intersect the graph more than once, it is NOT a function.

5. Using the vertical line test, which are functions and why?1 2 3
Yes
Yes No 4 5 6 No No
Yes

6. Let’s look at finding the domains and ranges for various graphs.

8. Graph, the determine Domain & Range

9. With equations, most of the time, the values for the domain are Real Numbers, and the values for the range are Real Numbers. HOWEVER, there are times when the domain and/or the range are/is restricted.
One of these instances is when there is a variable in the denominator. We have to restrict the domain to only those values that would not make the denominator undefined.
Special Note: A fraction is in two parts, right? The denominator is all important-the description, the name, the denomination, the size!
The numerator? Just how many you have!

10. Identify the domain and range:
Asymptote: a “border” that the graph gets infinitely close to.
Identify the domain and range: 1. 2. 3. 4.
What is the difference between #4 and the others?

11. * Restricted Domain in the denominator
Remember, f(x) means the function evaluated at x, it is the same as “y” and they can replace each other.
For Example: *
Set denominator ≠ 0 with rational eq’ns.
Reads: “D equals all x’s such that x is not equal to zero.”
The value for the domain CANNOT be 0 because that would make the denominator undefined. Notice, the numerator is unaffected.

13. Now, let’s look at the graph

14. -20 20

15. What would the graph look like? Asymptotes?

17. Try: Find the domains of the given functions.
2x – 3 ≠ 0
Denominator
x2 – 25 ≠ 0
2x ≠ 3
(x + 5) (x – 5) ≠ 0
and
x2 ≠ 25
x ≠ 5 or x ≠ -5

18. Active Learning Assignment: Be tough minded, but tender hearted.
P 122: (CE) 11-13, (WE)1-6, 9, 10
For & 1-6, just say “Yes” or “No” as to whether it is a function or not. For 9 & 10, show the algebraic solution. To see the graph, you may also use
WOW:
Be tough minded, but tender hearted.