Are these Functions notes free?

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What does the Functions revision sheet cover?

Function, Domain, Co-domain, Range, One-one and onto, The four combinations, one-one, not onto, onto, not one-one, neither one-one nor onto, Worked: evaluating a function, Six ways to represent a function, Shapes of the basic functions, Domain and range, basic functions, Worked: domain and range of a square-root function, Algebra of functions.

Is this for Class 11 Maharashtra HSC Mathematics?

Yes, it is written for the Maharashtra HSC Mathematics syllabus.

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Functions — Class 11 Maharashtra HSC Mathematics revision notes

A 5-page visual revision sheet for Functions, written for Class 11 Maharashtra HSC Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.

Functions revision notes, page 1 of 5 — A preview of page 1 — all 5 pages open full size in the app.

Functions in one look

one rule, one output for every input: domain, range and the shapes that follow

Function, Domain, Co-domain, Range

a function f:Ato B sends each x in A to exactly one y in B, y=f(x)
A is the domain of f, B the co-domain, y is the image of x
range = f(A): every y actually hit, always a subset of the co-domain
vertical line test: no vertical line may cut the graph of a function twice
horizontal line test: no horizontal line may cut the graph twice, so f is one-one

One-one and onto

one-one (injective): different elements of A have different images, f(a)=f(b)⇒ a=b
onto (surjective): every y in B is the image of some x in A, so f(A)=B
range of f = f(A) subset co-domain of f, with equality exactly when f is onto

The four combinations

one-one, not onto: every arrow lands on a different target, but some targets are unused
one-one and onto: a bijection: every target hit exactly once
onto, not one-one: every target is hit, but some target is hit twice
neither one-one nor onto: some target unused, another hit more than once

Worked: evaluating a function

Q. if f(x)=2x^2-3x+4, find f(7) and f(-2t)

f(7)=2(7)^2-3(7)+4=2(49)-21+4
=98-21+4=81
f(-2t)=2(-2t)^2-3(-2t)+4=2(4t^2)+6t+4

Answer: f(7)=81, f(-2t)=8t^2+6t+4

Six ways to represent a function

verbal: a sentence describing the rule, e.g. output exceeds twice the input by 1
arrow/Venn diagram: domain and range as two ovals joined by arrows
ordered pairs: pairs like (2,5),(3,7),(4,9),(5,11); domain is the 1st entries, range the 2nd
rule/formula: y=f(x)=2x+1, with a stated domain
tabular: a two-row table of x and y values
graphical: domain is the graph's projection on the X-axis, range its projection on the Y-axis

Page 1 of 5. The full sheet, all 5 pages, opens free in the app.

What this Functions sheet covers

Function, Domain, Co-domain, Range
One-one and onto
The four combinations
one-one, not onto
onto, not one-one
neither one-one nor onto
Worked: evaluating a function
Six ways to represent a function
Shapes of the basic functions
Domain and range, basic functions
Worked: domain and range of a square-root function
Algebra of functions
Composition of functions
Worked: composing two functions
Inverse functions
Worked: evaluating an inverse from a value
Signum and modulus (piecewise-defined) functions
Greatest integer and fractional part functions
Worked: solving with the modulus function
Traps that cost marks
Tricks that save time

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