Graph y=3tan(x)

Problem

y=3*tan(x)

Solution

1. Identify the parent function and its properties. The parent function is y=tan(x) which has a period of π and vertical asymptotes at x=π/2+n*π for any integer n

2. Determine the transformation applied to the parent function. The coefficient 3 in y=3*tan(x) represents a vertical stretch by a factor of 3

3. Find the asymptotes for the transformed function. Since there is no horizontal shift or change in period, the vertical asymptotes remain at x=−π/2 x=π/2 x=(3*π)/2 and so on.

4. Identify key points within one period, typically (−π/4,π/4) For y=3*tan(x) when x=π/4 y=3*tan(π/4)=3*(1)=3 When x=−π/4 y=3*tan(−π/4)=3*(−1)=−3 The x-intercept remains at (0,0)

5. Sketch the graph by plotting the points (−π/4,−3) (0,0) and (π/4,3) then drawing the characteristic tangent curves approaching the vertical asymptotes.

Final Answer

y=3*tan(x)

Want more problems? Check here!