Which of the following statements are correct?
(A) The graph of an increasing function slopes downward.
(B) In a function y = f(x), each value of x gives a unique value of y.
(C) In the demand function X = f(P), X is the dependent variable.
(D) y = 5 + x is a decreasing function.
(E) For a decreasing function, y does not increase as x increases.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (B), (C) and (E) only
A function y = f(x) gives one value of y for each value of x. It is increasing if y does not fall as x rises, and decreasing if y does not rise as x rises.
(A) The graph of an increasing function slopes downward. — Incorrect. An increasing function has an upward sloping graph.
(B) In a function y = f(x), each value of x gives a unique value of y. — Correct. This is what makes it a function.
(C) In the demand function X = f(P), X is the dependent variable. — Correct. The quantity X depends on the price P.
(D) y = 5 + x is a decreasing function. — Incorrect. As x rises, y = 5 + x rises, so it is an increasing function.
(E) For a decreasing function, y does not increase as x increases. — Correct. This is the meaning of a decreasing function.
NCERT (2026-27): “Functions Consider any two variables x and y. A function y = f (x) is a relation between the two variables x and y such that for each value of x, there is an unique value of the variable y. In other words, f (x) is a rule which assigns an unique value y for each value of x. As the value of y depends on the value of x, y is called the dependent variable and x is called the independent variable.” “A function y = f (x) is an increasing function if the value of y does not decrease with increase in the value of x. It is a decreasing function if the value of y does not increase with increase in the value of x. The function in Example 1 is an increasing function. So is the function y = x + 5. …” “Graphical Representation of a Function … The graph of an increasing function is upward sloping or and the graph of a decreasing function is downward sloping. …” |