# How do you graph #y= tan (2x)#?

##### 1 Answer

Here's the graph (mousewheel to zoom):

graph{tan(2x) [-5, 5, -2.5, 2.5]}

#### Explanation:

The graph is just like tan(x), but 2 times faster. It has period

Generally for any fancy function

For real number

- graph of
#f(ax)# is squeezed horizontally (clock is faster) - graph of
#f(x/a)# is stretched horizontally (clock is slower) - graph of
#af(x)# is stretched vertically - graph of
#f(x)/a# is squeezed vertically

And for positive real number

- graph of
#f(x+b)# is shifted left (clock is ahead of time) - graph of
#f(x-b)# is shifted right (clock is delayed) - graph of
#f(x)+b# is shifted up - graph of
#f(x)-b# is shifted down

Please ask if any clarifications are needed.