graph of y=tan(x) | Summary and Q&A

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July 19, 2016
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blackpenredpen
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graph of y=tan(x)

TL;DR

Learn how to graph the function y=tan(x) by finding its domain, identifying vertical asymptotes, and understanding its shape.

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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 x-axis, 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 set-builder notation?

The domain of y=tan(x) can be represented using set-builder 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 x-axis and incorporating the vertical asymptotes. The key features of the graph, such as zero points and shape, are explained.

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