Graph y=-4tan(x)

Problem

y=−4*tan(x)

Solution

1. Identify the parent function and its properties. The function is a transformation of 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 period of the function. Since there is no horizontal stretch or compression (the coefficient of x is 1, the period remains P=π

3. Identify the vertical asymptotes. The asymptotes occur where the tangent function is undefined. For this function, they are located at x=−π/2 and x=π/2 for the primary cycle.

4. Analyze the vertical stretch and reflection. The coefficient −4 indicates a vertical stretch by a factor of 4 and a reflection across the xaxis. Instead of increasing from left to right, the graph will decrease.

5. Plot key points within one period.
   At x=−π/4 y=−4*tan(−π/4)=−4*(−1)=4
   At x=0 y=−4*tan(0)=0
   At x=π/4 y=−4*tan(π/4)=−4*(1)=−4

6. Sketch the curve passing through the points (−π/4,4) (0,0) and (π/4,−4) approaching the vertical asymptotes at x=±π/2

Final Answer

To graph y=−4*tan(x) plot vertical asymptotes at x=π/2+n*π and draw a decreasing tangent curve passing through (0,0) with a vertical stretch factor of 4

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