Without looking at a graph?

Sure.

[Time will come, (when you are comfortable with Trigonometry already) when you don't have to look at graphs to analyze trig equations. Well, maybe seldom only.]

y = -3 tan 2x

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when x = - pi/8,

y = -3 tan 2(-pi/8)

y = -3 tan -pi/4

angle -pi/4 is in the 4th quadrant.

Its reference angle is pi/4 (or 45 degrees). I assume you know by heart the tan(pi/4) or tan(45deg). It is 1.

Since -pi/4 is in the 4th quadrant, where tangent is negative (you know that?), then,

y = -3 *(-1)

y = 3 ----answer

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when x = 0

y = -3 tan 2*0

y = -3 tan 0

tan(0) is 0, so,

y = -3 * 0

y = 0 -----answer.

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when x = pi/8

y = -3 tan 2(pi/8)

y = -3 tan pi/4

Angle pi/4 (or 45 deg) is in the 1st quadrant.

You know that tan(pi/4) or tan(45deg) is 1.

So,

y = -3 *(1)

y = -3 ----answer