Statistics · Class 11 Commerce
Ch 8Function — Class 11 Statistics, concept-first.
Gujarat Std 11 Commerce students meet the idea of a function through the more general idea of a relation between two sets. Understanding this distinction carefully is the foundation for everything else in this chapter — and for the correlation, regression and probability chapters that follow in Std 12 Statistics.
Key concepts
Hover a concept to preview it and jump to its most relevant Q&A.
Relation and Function
A relation from set to set is any subset of the Cartesian product — it pairs some elements of with some elements of using any rule at all.
Most relevant Q&A
Chapter contents
The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.
Relations and Functions — Meaning and Definition
Gujarat Std 11 Commerce students meet the idea of a function through the more general idea of a relation between two sets.
Domain, Co-domain and Range
For a function :
Types of Functions
Functions can be classified in two independent ways: by how inputs map to outputs (one-one, many-one, onto, into), and by the algebraic form of the rule (constant, linear, quadratic, polynomial).
Linear and Quadratic Functions and Their Graphs
A linear function has the form
Functions in Business — Cost, Revenue, Demand and Profit
A firm's total cost function expresses total cost as a function of output :
Exercises
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- Q7The marks scored by five students in a business mathematics test are given below: | Roll No. (x) | 1 | 2 | 3 | 4 | 5 | |---|---|---|---|---|…Free
- Q8Let $A = \{1, 2, 3\}$ and $B = \{a, b, c, d\}$. Examine each of the following relations from $A$ to $B$ and state whether it is a function;…Free
- Q9Find the domain and range of the function $f(x) = \sqrt{x - 3}$.Free
- Q10The demand function for a good is $Q_d = 200 - 4P$ and the supply function is $Q_s = -40 + 6P$, where $P$ is the price in ₹ and $Q$ is the q…Preview
- Q11A firm's revenue function is $R(x) = 100x - 2x^2$. (i) Find the output level at which revenue is maximised, and the maximum revenue. (ii) Fi…Preview
- Q12A firm's total cost function is $C(x) = 3000 + 25x + 0.5x^2$, where $x$ is the number of units produced. Using this function, find (i) the t…Preview
- Q13Which of the following relations from $A = \{1, 2, 3\}$ to $B = \{p, q, r\}$ is a function? (a) $\{(1,p), (1,q), (2,r), (3,p)\}$ (b) $\{(1,p…Preview
- Q14The domain of the function $f(x) = \dfrac{1}{x+5}$ is: (a) $\mathbb{R}$ (b) $\mathbb{R} - \{5\}$ (c) $\mathbb{R} - \{-5\}$ (d) $\mathbb{R} -…Preview
More questions
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- Example 1Let $A = \{1, 2, 3, 4\}$ and $B = \{2, 4, 6, 8, 10\}$. A relation $R$ from $A$ to $B$ is defined by the rule $y = 2x$, giving $R = \{(1,2),…Free
- Example 2Find the domain and range of (i) $f(x) = \dfrac{1}{x-3}$ (ii) $g(x) = x^2$, for $x \in \mathbb{R}$.Free
- Example 3The demand function for a commodity is $Q_d = 120 - 3P$, where $Q_d$ is the quantity demanded and $P$ is the price in ₹. (i) State whether t…Preview
- Example 4A firm's total revenue function is $R(x) = 40x - x^2$, where $x$ is the number of units sold. (i) Show that $R(x)$ is a quadratic function o…Preview
- Example 5A company's total cost function is $C(x) = 2500 + 45x$, where $x$ is the number of units produced. (i) Identify the fixed cost and the varia…Preview
- Example 6For a certain product, the revenue function is $R(x) = 60x$ and the cost function is $C(x) = 20x + 8000$, where $x$ is the number of units s…Preview