Vertical and Horizontal Transformation - Practice Questions & MCQ

Vertical shift $f(x) \rightarrow f(x) \pm a$
A vertical shift of a function occurs if we add or subtract the constant to the function $y=f(x)$
For $a>0$, the graph of $y=f(x)+a$ is obtained by shifting the graph of $f(x)$ upwards by 'a' units, whereas the graph of $y=f(x)-a$ is obtained by shifting the graph of $f(x)$ downwards by 'a' units.

For Example:
The graph of the function $f(x)=x^2+4$ is the graph of $f(x)=x^2$ shifted up by 4 units;
The graph of the function $f(x)=x^2-4$ is the graph of $f(x)=x^2$ shifted down by 4 units.

Horizontal shift: $f(x) \rightarrow f(x \pm a)$

A horizontal shift of a function occurs if we add or subtract the same constant to each input $x$.
For $a>0$, the graph of $y=f(x+a)$ is obtained by shifting the graph of $f(x)$ to the left by 'a' units.
The graph of $y=f(x-a)$ is obtained by shifting the graph of $f(x)$ to the right by 'a' units.
For Example

$
f(x)=|x+3|
$
The graph of $f(x)=|x+3|$ is the graph of $y=|x|$ shifted leftwards by 3 units. Similarly, the graph of $f(x)=|x-3|$ is the graph of $y=|x|$ shifted rightward by 3 units