Questions: Identify the function whose graph appears above. It is either: f(x) = A tan(x) + k or it is f(x) = A cot(x) + k.

Solution Steps

The graph resembles the tangent function. The tangent function has vertical asymptotes at odd multiples of π/2. This graph has asymptotes at -π/2, π/2, and 3π/2, which are odd multiples of π/2.

Since the graph passes through the origin (0,0), the vertical shift \(k\) is 0. The graph increases from left to right, indicating that the coefficient \(A\) of the tangent function is positive. The graph appears to have a period of π, which is the standard period for tangent. Since the points (π/4, 1) and (-π/4, -1) are on the graph and tan(π/4) = 1, it appears that A=1.

Final Answer