How do you graph #y=3tan(1/2x)-2#?

Answer 1

As below.

#y = 3 tan (x/2) - 2#
Standard form of tangent function is #y = A tan(Bx - C) + D#
#A = 3, B = 1/2, C = 0, D = -2#
#Amplitude = NONE # for tangent function.
Period #= (pi) / |B| = pi / (1/2) = 2pi#
Phase Shift #= (-C) / B = 0#
Vertical Shift #= D = -2#

graph{3 tan(x/2) - 2 [-10, 10, -5, 5]}

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Answer 2

To graph the function y = 3tan(1/2x) - 2, follow these steps:

  1. Identify the key characteristics of the tangent function: it has vertical asymptotes where the denominator becomes zero, and its period is π.

  2. Determine the vertical asymptotes by setting the denominator of the tangent function equal to zero: 1/2x = kπ, where k is an integer.

  3. Solve for x to find the locations of the vertical asymptotes.

  4. Plot these vertical asymptotes on the x-axis.

  5. Find the period of the function, which is π. This means that the function repeats every π units.

  6. Choose points to the left and right of each vertical asymptote, and calculate their y-values using the function.

  7. Plot these points on the graph.

  8. Connect the points smoothly to represent the graph of the function between each pair of vertical asymptotes.

  9. Note that the graph of the tangent function has a horizontal shift due to the coefficient 1/2 in the argument. This shift depends on the value of 1/2x.

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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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