Question

How do you graph `y=2tanx`?

Answer 1

When a coefficient is present in the function like in this case is 2, the transformation rule states that you should multiply the result of tanx by 2.
In the case of tanx
When you did tan45, the outcome was 1.
Now as the function is 2tanx, the out come is 1*2 i.e 2.

SO the graph is, you multiply the values of y of tan x with 2 and it becomes ;
graph{2tanx [-12.65, 12.65, -6.32, 6.33]}
For example if a function is
f(x) = x
when x=0 , f(x) =0
x=1 , f(x) = 1
x=2 , f(x) =2
then the graph is straight line making 45 degrees to the x axis and passing through the origin.

Now you have
F(x) = 2x
In this case,
when x=0 , f(x) =0
x=1 , f(x) = 2
x=2 , f(x) =4

SO the graph has become more steep .