Question

Print out the graph paper from the "Let's Review" section. Sketch the graph of y = 2tanx for -pi/2 ≤ x ≤ pi/2

and turn it into your teacher. Indicate the asymptotes, if any.

In the box below, describe similarities and differences between the graphs of y = 2tanx and y = tanx.

Answer 1

The graph is attached below.

Same asymptote as similarity and the slopes are different.

Explanation:

We need to find the graph of
`y = 2 * tanx.......... (-\pi )/(2) \leq  x \leq (\pi )/(2)`

When
`x = 0; y = 0\\x = (\pi )/(4) ; y = 2\\x = - (\pi )/(4) ; y = -2`

and
`\lim_{x \to (\pi )/(2) } y =  \infty\\ \lim_{x \to - (\pi )/(2) } y = - \infty`

The asymptotes are
`x = (\pi )/(2) \\ x = - (\pi )/(2)`

If we compare the graphs of
`y = 2 * tanx.....(1)\\y = tanx`......(2)

then the similarities are, they have same asymptote.

Difference between them is the rate of change that is the slope of the equations.