Graph y=-tan(x)

Problem

y=−tan(x)

Solution

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

2. Determine the transformation applied to the parent function. The negative sign in front of the function, y=−tan(x) represents a reflection across the xaxis.

3. Identify key points for one period of the parent function between the asymptotes x=−π/2 and x=π/2 The points (−π/4,−1) (0,0) and (π/4,1) are standard for y=tan(x)

4. Apply the reflection to these key points by multiplying the ycoordinates by −1 The new points for y=−tan(x) are (−π/4,1) (0,0) and (π/4,−1)

5. Sketch the graph by drawing the vertical asymptotes at x=…,−(3*π)/2,−π/2,π/2,(3*π)/2,… and plotting the reflected points. The curve will decrease from left to right between each pair of asymptotes.

Final Answer

y=−tan(x)

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