Describe how to find the domain and range for the tangent function.

To find the domain of the tangent function, you need to remember that tangent is defined as the ratio of sine to cosine (tan(x) = sin(x)/cos(x)). This means the function is undefined when cos(x) = 0, which occurs at odd multiples of π/2 (like ±π/2, ±3π/2, etc.). Therefore, the domain of the tangent function is all real numbers except those where x = (2n + 1)π/2, where n is any integer. For the range, it's a little more straightforward! The tangent function can take on any real number value, so its range is all real numbers (-∞, ∞). You can visualize this by looking at the behavior of the tangent function as it approaches its vertical asymptotes at odd multiples of π/2—it goes to positive infinity on one side and negative infinity on the other, encompassing all possible y-values!