Question

How is the asymptote for a tangent graph found?

a) At x = 0
b) By analyzing the critical points
c) There is no asymptote for the tangent graph
d) At x = ±π/2

Answer 1

The asymptote for a tangent graph is found at x = ±π/2.

Step-by-step explanation:

The asymptote for a tangent graph can be found at d) At x = ±π/2.

When we look at the tangent function, we can observe that it has vertical asymptotes at x = ±π/2. This means that as x approaches ±π/2, the tangent function approaches positive or negative infinity.

For example, when x = π/2, the tangent function is undefined because it would involve dividing by zero. However, as x approaches π/2 from the left side, the values of the tangent function increase without bound, approaching positive infinity. Similarly, as x approaches π/2 from the right side, the values of the tangent function decrease without bound, approaching negative infinity.