At what value of x does the function y = tan(x) have a vertical asymptote?

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Question: At what value of x does the function y = tan(x) have a vertical asymptote?

Options:

Correct Answer: π/2

Solution:

The tangent function has vertical asymptotes at x = π/2 + nπ, where n is an integer. The first asymptote in [0, π] is at π/2.

At what value of x does the function y = tan(x) have a vertical asymptote?

At what value of x does the function y = tan(x) have a vertical asymptote?

Step 1: Understand what a vertical asymptote is. A vertical asymptote is a line where the function goes to infinity or negative infinity.
Step 2: Know the function we are working with, which is y = tan(x).
Step 3: Recall that the tangent function is undefined at certain points, which leads to vertical asymptotes.
Step 4: The tangent function has vertical asymptotes at x = π/2 + nπ, where n is any integer (like 0, 1, -1, etc.).
Step 5: For n = 0, the first vertical asymptote is at x = π/2.
Step 6: If you want to find more vertical asymptotes, you can substitute different integer values for n.

Tangent Function Asymptotes – The tangent function has vertical asymptotes where its denominator (cos(x)) is zero, specifically at x = π/2 + nπ, where n is any integer.