Assertion Reasoning Quiz

Assertion (A): The domain of the rational function \(f(x) = \frac{1}{x - 2}\) is \(\mathbb{R} - \{2\}\).

Reason (R): A rational function of the form \(\frac{p(x)}{q(x)}\) is defined for all real numbers except those where the denominator \(q(x) = 0\).

Assertion (A): The range of the function \(f(x) = x^2\) is the set of all non-negative real numbers, \([0, \infty)\).

Reason (R): The domain of the function \(f(x) = x^2\) is the set of all real numbers \(\mathbb{R}\).

Assertion (A): For \(A=\{1,2,3,4,5,6\}\) and \(R=\{(x,y):y=x+1,\ x,y\in A\}\), the domain of \(R\) is \(\{1,2,3,4,5\}\).
Reason (R): The codomain of \(R\) is \(\{2,3,4,5,6\}\).

Assertion (A): A school offers 4 clubs and 3 activity periods. If a student’s choice is recorded as ⟨club, period⟩, then there are 12 possible ordered choices.
Reason (R): Every club can be paired with each of the 3 activity periods.

Assertion (A): The range of the constant function \(f(x) = 5\) for all real \(x\) is the singleton set \(\{5\}\).

Reason (R): A constant function \(f(x) = c\) maps all elements of its domain to the same single constant value \(c\).