Simulation · Maths · Class 11
Relation or function?
"Relation or function?" is a free, interactive Class 11 Maths simulation for JEE, built on the lesson "Functions" in Relations and Functions. Tap a student, then tap a row, to draw an arrow from that student to that row. Tap the same pair again to remove it. The readouts track the domain, the range and whether you have a function. A relation is any set of arrows: 4 × 5 = 20 possible pairs, so 2²⁰ relations. A function needs one arrow out of every student: 5 choices each, so 5⁴ = 625 functions.
From the lesson Functions in Relations and Functions. Change the values and watch what happens.
Relation or function?Maths · Class 11
The idea behind it
NCERT §2.4
- A function f from A to B is a relation from A to B in which every element of A has one and only one image in B. Equivalently, the domain of f is the whole of A and no two different pairs of f share a first entry.
- We write f : A → B and f(x) = y when (x, y) ∈ f. y is the image of x under f, and x is a preimage of y.
- A is the domain of f and B its codomain. The range of f is the set of all images, and range ⊂ codomain.
- The test has two parts: no element of A is left without an arrow, and no element of A sends two arrows. Several elements of A may share an image, and some elements of B may receive no arrow at all.
- Every function is a relation, but a relation is a function only when it passes both parts of the test. {(1, 3), (2, 3), (3, 5)} is a function on {1, 2, 3}; {(1, 4), (1, 6), (2, 6)} is not, because 1 has two images.
- A function whose range is R or a subset of R is a real valued function. If its domain is also R or a subset of R, it is a real function.
- Evaluating a real function means substituting into its rule: for f(x) = 3x − 4, f(0) = −4, f(2) = 2 and f(−1) = −7.
- Counting result: when n(A) = p and n(B) = q, each of the p elements of A picks one of q images independently, so there are qᵖ functions from A to B.
Questions
2 answers
- What does the "Relation or function?" simulation show?
- Tap a student, then tap a row, to draw an arrow from that student to that row. Tap the same pair again to remove it. The readouts track the domain, the range and whether you have a function.
- Is this simulation free?
- Yes. It is free and runs in the browser on a phone or a laptop. It belongs to the lesson "Functions" in Relations and Functions (Class 11 Maths).
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