graph of y=tan(x)  Summary and Q&A
TL;DR
Learn how to graph the function y=tan(x) by finding its domain, identifying vertical asymptotes, and understanding its shape.
Questions & Answers
Q: How do you find the domain of the tangent function?
To find the domain of y=tan(x), we need to ensure that the denominator, cosine x, is not zero. By using the unit circle, we can determine that the vertical asymptotes occur at x values of pi/2, 3pi/2, 5pi/2, etc.
Q: How do you graph the function y=tan(x)?
To graph y=tan(x), start by plotting the x values on the xaxis, including the vertical asymptotes. Remember that the shape of the graph approaches the vertical asymptotes. You can also identify key points like (0, 0) and (pi/4, 1) to help sketch the curve.
Q: What is the range of the tangent function?
The range of y=tan(x) is from negative infinity to positive infinity. This is because the graph goes infinitely down as it approaches the vertical asymptotes and infinitely up as it moves away from the asymptotes.
Q: How can I represent the domain of the tangent function using setbuilder notation?
The domain of y=tan(x) can be represented using setbuilder notation as follows: X is not equal to k*pi/2, where k is any odd integer.
Summary & Key Takeaways

The video teaches how to find the domain of the tangent function, which requires ensuring that the denominator (cosine x) is not zero.

Using the unit circle, the values for x where cosine is zero (vertical asymptotes) are determined, such as pi/2, 3pi/2, 5pi/2, etc.

The graph of y=tan(x) is drawn by plotting the values on the xaxis and incorporating the vertical asymptotes. The key features of the graph, such as zero points and shape, are explained.