Question of the Day In real Analysis

$latex \mathbf{Question:} \text{ Let } f_n \to f \text{ pointwise at every point in the interval } [a,b] .\\

\text{ And } f_n \text{ is continuous }. \text{ Which of the is/are true ?} \\ \\

1. \text{ If each } f_n \text{ is increasing on } [a,b], \text{ then so is } f\\

2. \text{ If each } f_n \text{ is bounded on }[a,b], \text{ then so is }f\\

3. \text{ If each } f_n \text { is everywhere discontinuous on } [a,b], \text { then so is } f\\

4. \text{ If each } f_n \text { is constant on } [a,b],  \text{ then so is } f

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