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Graph y=tan(x)+2

Problem

y=tan(x)+2

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 equation y=tan(x)+2 represents a vertical shift of the graph of y=tan(x) upward by 2 units.

  3. Locate the new center points of the graph. In the parent function, the graph passes through (0,0) After the vertical shift, the center point of one period moves to (0,2)

  4. Identify the vertical asymptotes, which remain unchanged by a vertical shift. The asymptotes for y=tan(x)+2 are located at x=−π/2 x=π/2 x=(3*π)/2 and so on.

  5. Plot key points within one period to determine the shape. For the interval (−π/2,π/2)

  • At x=−π/4 y=tan(−π/4)+2=−1+2=1

  • At x=0 y=tan(0)+2=0+2=2

  • At x=π/4 y=tan(π/4)+2=1+2=3

  1. Sketch the curves between the asymptotes, ensuring the graph passes through the points (−π/4,1) (0,2) and (π/4,3) following the characteristic "S" shape of the tangent function.

Final Answer

y=tan(x)+2

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