Question

Is the graph of y=3tanx affecting it vertically or horizontally? As in is the 3 in front of the tangent function transforming the normal tangent graph by a vertical stretch or horizontal stretch?

Answer 1

Vertical stretch.

Consider any point on the graph \(y = \tan{x}\), say at \(x = \pi/4\).
\((x,y) = (\pi/4, 1)\)

now for the same value of \(x\), the new value of \(y = 3\).
So you have a vertical stretch that's 3 times the initial value

Answer 2

So you're saying that essentially I can leave the points where the tan graph crosses the x axis as they are, but change the units on the point (pi/4,1) to be (pi/4,3)?
Thanks for the help by the way.

Answer 3

Yes.
Every point on the graph gets stretched 3 times. Obviously, the crossings with the x-axis remains the same (as y = 0, so stretching has no effect).

Answer 4

I see. Thank you!