Graph f(x)=tan(x)

Problem

ƒ(x)=tan(x)

Solution

1. Identify the domain and vertical asymptotes by finding where cos(x)=0 since tan(x)=sin(x)/cos(x) Vertical asymptotes occur at x=π/2+n*π for any integer n

2. Determine the period of the function. The tangent function has a period of π meaning the graph repeats every π units along the x-axis.

3. Find the x-intercepts by solving sin(x)=0 The graph crosses the x-axis at x=n*π for any integer n

4. Identify key points within one period, such as (−π/4,−1) (0,0) and (π/4,1) to determine the shape of the curve.

5. Sketch the curves between the vertical asymptotes. The function is increasing on all intervals where it is defined, approaching +∞ as x approaches an asymptote from the left and −∞ from the right.

Final Answer

ƒ(x)=tan(x)

Want more problems? Check here!