What is the primary characteristic of a tangent graph?

The primary characteristic of a tangent graph is that it contains vertical asymptotes. This is because the tangent function is defined as the ratio of the sine to the cosine function, specifically tan(x) = sin(x) / cos(x). Vertical asymptotes occur at the points where the cosine function equals zero, which happens at odd multiples of 90 degrees (or π/2 radians). At these points, the tangent function approaches infinity, indicating the presence of vertical asymptotes in the graph.

The presence of vertical asymptotes is a key feature that distinguishes the tangent graph from other trigonometric functions. This characteristic shows the behavior of the graph as it approaches those undefined points, where the function tends to positive or negative infinity.

The other characteristics mentioned in the options do not accurately describe the tangent function. For instance, while it's true that the tangent function can take on all real values, it does not oscillate between -1 and 1, nor does it have a period of 180 degrees; instead, the period of the tangent function is actually 360 degrees. Additionally, the graph is not always positive; it varies across its period and can definitely take on negative values depending on the input.