domain and interval notation. domain the set of all possible input values (generally x values) we...
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Domain The set of all possible input values (generally x
values) We write the domain in interval notation Interval notation has 2 important components:
Position Symbols
Interval Notation – Position Has 2 positions: the lower bound and the
upper bound
[4, 12)Lower Bound
• 1st Number
• Lowest Possible x-value
Upper Bound
• 2nd Number
• Highest Possible x-value
Interval Notation – Symbols
[ ] → brackets
Inclusive (the number is included)
=, ≤, ≥ ● (closed circle)
( ) → parentheses
Exclusive (the number is excluded)
≠, <, > ○ (open circle)
[4, 12) Has 2 types of symbols: brackets and parentheses
Understanding Interval Notation4 ≤ x < 12
Interval Notation:
How We Say It: The domain is 4 to
12 .
On a Number Line:
Example – Domain: –2 < x ≤ 6 Interval Notation:
How We Say It: The domain is –2 to
6 .
On a Number Line:
Example – Domain: –16 < x < –8 Interval Notation:
How We Say It: The domain is –16 to
–8 .
On a Number Line:
Example – Domain: x is Interval Notation:
How We Say It: The domain is to
On a Number Line:
all real numbers
Combining Restricted Domains When we have more than one domain restriction,
then we need to figure out the interval notation that satisfies all the restrictions
Examples: x ≥ 4, x ≠ 11 –10 ≤ x < 14, x ≠ 0
Combining Multiple Domain Restrictions, cont.1. Sketch one of the domains on a number line.
2. Add a sketch of the other domain.
3. Write the combined domain in interval notation. Include a “U” in between each set of intervals (if you have more than one).
Answers1. (–2, 7) 6. (–∞,4)2. (–3, 1] 7. (–1, 2) U (2, ∞)3. [–9, –4] 8. [–5, ∞)4. [–7, –1] 9. (–2, ∞)5. (–∞, 6) U (6, 10) U (10, ∞)
*Solving for Restricted Domains Algebraically In order to determine where the domain is
defined algebraically, we actually solve for where the domain is undefined!!!
Every value of x that isn’t undefined must be part of the domain.
*Solving for the Domain Algebraically
In my function, do I have a square root? Then I solve for the domain by: setting the
radicand (the expression under the radical symbol) ≥ 0 and then solve for x
*Solving for the Domain Algebraically
In my function, do I have a fraction? Then I solve for the domain by: setting the
denominator ≠ 0 and then solve for what x is not equal to.
*Solving for the Domain Algebraically
In my function, do I have neither? Then I solve for the domain by: I don’t have
to solve anything!!! The domain is (–∞, ∞)!!!
*Solving for the Domain Algebraically
In my function, do I have both? Then I solve for the domain by: solving for each
of the domain restrictions independently
Your Turn:
Complete problems 1 – 10 on the “Solving for the Domain Algebraically” handout
#8 – Typo!6xx
1)x(f 2
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