Question

review the graph. which function is represented in the graph? y = tanx y = cosx y = tan⁻¹x y = cos⁻¹x

Explanation:

Step1: Recall function properties

The function \(y = \tan x\) has vertical - asymptotes and its range is \((-\infty,\infty)\). The function \(y=\cos x\) has a range of \([- 1,1]\) and is periodic. The function \(y = \tan^{-1}x\) has a range of \((-\frac{\pi}{2},\frac{\pi}{2})\) and is an increasing function. The function \(y=\cos^{-1}x\) has a range of \([0,\pi]\) and is a decreasing function.

Step2: Analyze the given graph

The graph has a range between \(-\frac{\pi}{2}\) and \(\frac{\pi}{2}\) and is an increasing function of \(x\).

Answer:

\(y = \tan^{-1}x\)