Domain and Range
Identify possible inputs first, then determine the outputs the function can actually produce.
Domain and Range
Not yet verified on this browser.
Domain means allowed inputs; range means resulting outputs
In an ordered pair (x,y), x belongs to the domain and y belongs to the range. Algebraic rules may exclude inputs: a denominator cannot be zero, and an even root must contain a nonnegative value when working with real numbers. Context can restrict inputs further.
Domain
Ask: Which x-values are permitted?
Range
Ask: Which y-values occur after the permitted inputs are used?
Input first, restriction second, outputs last
Problem: Find the domain of f(x)=1(x−3).
Recognize: Division by zero is undefined.
Do it fast: x−3=0 at x=3, so exclude 3. Every other real input is allowed.
Why it works
Restrictions come from operations in the rule or limits in the context; they are not arbitrary values to memorize.
Five forms you should recognize
For (1,4), (2,6), (3,6), the domain is {1,2,3}; the range is {4,6}. Repeated outputs are listed once.
For 1(x−5), x=5 is excluded because it makes the denominator zero.
For √(x−2), require x−2≥0, so x≥2.
Project graph points horizontally to read x-values and vertically to read y-values. Open endpoints are not included.
If tickets are numbered 1 to 100, the meaningful domain is those whole numbers—not all real numbers.
Check before you commit
- Switching domain and range
- Listing repeated outputs more than once
- Allowing a zero denominator
- Forgetting square-root restrictions
- Ignoring open endpoints
- Using all real numbers despite a contextual limit
Do you need the lesson-or just practice?
One original question in each form recommends your next step. It does not yet verify mastery.
Work at the level you need.
Foundations
Build the core procedure with immediate explanations.
Core Practice
Use mixed forms with less scaffolding.
UPCAT-Style Transfer
Apply the competency in unfamiliar representations.
Ready to verify this competency?
A score of 5/5 verifies mastery. An unsuccessful attempt loads a different five-form bank.
Domain and Range FAQ
Why are there two mastery sets?
An unsuccessful attempt loads a different five-question set so memorizing one set does not verify mastery.
Does 5/5 mean permanent mastery?
It verifies the competency today. Revisit it later through mixed practice and simulations.
Continue your mathematics review.
Your progress stays on this browser.
Mastery results save to your Teacher Abi study profile.
Return to Student Hub View UPCAT Coverage
No comments:
Post a Comment