With reference to a function y = f(x), which of the following statements is NOT correct?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → y = 50 – x is an increasing function.
In a function y = f(x), x is the independent variable and y depends on it. A function is decreasing if y does not rise when x rises.
Option (1) x is called the independent variable. — True. y depends on x, so x is the independent variable.
Option (2) y = 50 – x is an increasing function. — False. In y = 50 − x, y falls as x rises, so it is a decreasing function.
Option (3) For each value of x, there is a unique value of y. — True. A function gives a unique value of y for each value of x.
Option (4) y is called the dependent variable. — True. Its value depends on x, so y is the dependent variable.
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 y = 50 – x is also decreasing.” |