Basic graph transformations for JEE

Formula

\[\begin{aligned}y=f(x-a)&\Rightarrow \text{shift right by }a,\\ y=f(x)+b&\Rightarrow \text{shift up by }b,\\ y=-f(x)&\Rightarrow \text{reflection in }x\text{-axis},\\ y=f(-x)&\Rightarrow \text{reflection in }y\text{-axis},\\ y=|f(x)|&\Rightarrow \text{portion below }x\text{-axis reflected above},\\ y=f(|x|)&\Rightarrow \text{right half mirrored to left}\end{aligned}\]

Variables: \(a,b\in\mathbb R\).

Sketching simple graphs and identifying continuity/differentiability points.