1. EXAMPLE 4 Graph a tangent function Graph one period of the function y = 2 tan 3x. SOLUTION b π = 3 π. The period is Intercepts: (0, 0) Asymptotes: x = 2b2b π = 2 3 π, or x = ; 6 π x = 2b2b π – = 2 3 π –, or x = ; 6 π –

2. EXAMPLE 4 Graph a tangent function Halfway points: (, a) 4b4b π = 4 3 π (, 2) = 12 π (, 2); (, – a) 4b4b π – = 4 3 π (, – 2) – = 12 π (, – 2) –

3. GUIDED PRACTICE for Example 4 Graph one period of the function. 10. y = 3 tan x SOLUTION

4. GUIDED PRACTICE for Example 4 Graph one period of the function. 11. y = tan 2x SOLUTION

5. GUIDED PRACTICE for Example 4 Graph one period of the function. 12. f (x) = 2 tan 4x SOLUTION

6. GUIDED PRACTICE for Example 4 Graph one period of the function. 13. g(x) = 5 tan πx SOLUTION