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Functions — Flashcards

ICSE · Class 12 · Mathematics

30 flashcards for Functions (ICSE Class 12 Mathematics) to test yourself on key terms and facts. Sample: "Check whether R = {(1, a), (2, c), (3, b)}"

101 questions30 flashcards14 formulas & key relations5 concepts

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A comprehensive infographic comparing different types of functions: one-one (injective), onto (surjective), many-one, into, and bijective, using set diagrams and clear definitions.
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30 Flashcards·
Basic Function TestDomain and RangeCounting FunctionsDomain of Rational FunctionDomain of Square Root FunctionRange of Square FunctionGraphical Test for Function
Card 1Basic Function Test

Check whether R = {(1, a), (2, c), (3, b)} from A = {1, 2, 3} to B = {a, b, c} is a function.

Answer

Step 1: Check each element of A. 1 maps to a. 2 maps to c. 3 maps to b. Step 2: Every element of the domain has exactly one image. Answer: R is a function.

Card 2Basic Function Test

Check whether R = {(1, a), (1, b), (3, c)} from A = {1, 2, 3} to B = {a, b, c} is a function.

Answer

Step 1: Look at element 1. It has two images: a and b. Step 2: A function cannot give two images to the same domain element. Answer: R is not a function.

Card 3Domain and Range

Find the domain, co-domain, and range of f = {(1, 5), (2, 6), (3, 7)} where f: A → B with A = {1, 2, 3} and B = {5, 6, 7, 8}.

Answer

Step 1: Domain is the set of first elements. Domain = {1, 2, 3} Step 2: Co-domain is the given target set. Co-domain = {5, 6, 7, 8} Step 3: Range is the set of actual images. Range = {5, 6, 7} Answer:…

Card 4Counting Functions

How many functions are possible from A to B if n(A) = 3 and n(B) = 4?

Answer

Use the formula: Number of functions from A to B = q^p. Here, p = 3 and q = 4. Step 1: Substitute values. 4^3 = 64 Answer: 64 functions.

Card 5Domain of Rational Function

Find the domain of f(x) = (x^2 + 2x + 1)/(x^2 - x - 6).

Answer

Step 1: Denominator cannot be zero. x^2 - x - 6 = (x - 3)(x + 2) Step 2: Set each factor not equal to zero. x - 3 ≠ 0 and x + 2 ≠ 0 So x ≠ 3 and x ≠ -2 Step 3: Write the domain. Answer: Domain = R - {…

Card 6Domain of Square Root Function

Find the domain of f(x) = sqrt(x - 3).

Answer

Step 1: The quantity inside the square root must be non-negative. x - 3 ≥ 0 Step 2: Solve the inequality. x ≥ 3 Answer: Domain = [3, ∞).

Card 7Range of Square Function

Find the range of f(x) = x^2 for x ∈ R.

Answer

Step 1: Square of any real number is never negative. x^2 ≥ 0 Step 2: The smallest value occurs at x = 0. f(0) = 0 Step 3: Larger values are possible for other real x. Answer: Range = [0, ∞).

Card 8Graphical Test for Function

Which curve represents a function: y = x^2 or y^2 = x? Give a reason.

Answer

For y = x^2: Each x has exactly one y value. So it represents a function. For y^2 = x: When x = 1, y = 1 or y = -1. So one x gives two y values. Answer: y = x^2 represents a function, but y^2 = x does…

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Frequently Asked Questions

What are the important topics in Functions for ICSE Class 12 Mathematics?
Key topics in Functions include Basic idea of a function, Standard real functions and their graphs, Domain and range of real functions, Graphical tests. Study these first, then practise questions on each for the ICSE Class 12 board exam.
How many flashcards are available for Functions?
There are 30 flashcards for Functions covering key definitions, facts and ideas. A few sample cards are shown on this page.
How should I revise Functions for the ICSE Class 12 board exam?
Learn the core ideas first, then work through the 101 practice questions on Functions. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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