Assertion Reasoning Quiz

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): The rule \[ h(x)=\begin{cases} x^2, & 0\le x\le2,\\ 2x, & 2\le x\le5 \end{cases} \] is not a function because \(x=2\) belongs to both intervals.
Reason (R): At \(x=2\), both formulas give the same value, namely \(4\).

Assertion (A): If the signum function is used to classify altitude as below, at or above sea level, then \(\operatorname{sgn}(-7)+\operatorname{sgn}(0)+\operatorname{sgn}(4)=0\).
Reason (R): The range of the signum function is \(\{-1,0,1\}\).

Assertion (A): A monitoring system has 3 sensors and 2 alert levels. The number of possible relations from the sensor set to the alert-level set is \(64\).
Reason (R): A relation is any subset of the Cartesian product, which here contains \(3\times2=6\) ordered pairs.

Assertion (A): The mapping shown below represents a function from the set of students to the set of lockers.
Reason (R): Every student has exactly one locker as image, although two different students may have the same locker as image.