How do you graph of the function #y=arctan(x)#?

Answer 1

#arctan(tan(x)) = x#

If we create a table of typical #x# and #tan(x)# values
and then modify the labels:

Plot the (modified label) table
and you should get something like:

graph{arctan(x) [-6.24, 6.247, -3.12, 3.12]}

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Answer 2

To graph the function y = arctan(x), follow these steps:

  1. Identify the key points:

    • The function approaches -π/2 as x approaches negative infinity.
    • The function approaches π/2 as x approaches positive infinity.
    • The function passes through the point (0, 0), as arctan(0) = 0.
  2. Draw the asymptotes:

    • There are vertical asymptotes at x = -∞ and x = +∞ due to the behavior of the function as x approaches these values.
  3. Plot the key points:

    • Plot the point (0, 0) as it is the y-intercept.
  4. Draw the curve:

    • The curve starts from negative infinity, approaches the y-axis from below, passes through the point (0, 0), and then approaches positive infinity while getting closer to the asymptote at y = π/2.
  5. Sketch the curve smoothly, keeping in mind its behavior as described above.

  6. Label the axes and any important points as necessary.

This results in a curve that starts near the origin, approaches the y-axis without touching it, and continues upward toward positive infinity. The curve never exceeds the range -π/2 to π/2 on the y-axis.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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