Problem

Use the graph of \(y~=~\tan(x)\) on \((-\pi~/2,~\pi~/2)\) to state the period, all zeros, vertical asymptotes, defined branches, monotonicity on each branch, and range.

Exact tangent graph on (−π/2,π/2) with radian ticks, endpoint conventions, all asymptotes, and complete branch arrows.

Big Picture

What this problem is really about

Tangent's graph is organized by the denominator in sine over cosine. Zeros of cosine create excluded vertical asymptotes, and each open interval between adjacent asymptotes contains one continuous increasing branch; zeros occur where sine vanishes while cosine does not. The repeating branch width gives the period, and its unbounded sweep gives the range.

Answer choices

Choose your path.

Preview only

The period is pi; zeros are 0; vertical asymptotes are -pi/2, pi/2; defined branches are (-pi/2, pi/2); tangent is strictly decreasing on every branch and has range (-infinity, infinity).

The period is 2pi; zeros are 0; vertical asymptotes are -pi/2, pi/2; defined branches are (-pi/2, pi/2); tangent is strictly increasing on every branch and has range (-infinity, infinity).

The period is pi; zeros are 0; vertical asymptotes are -pi/2, pi/2; defined branches are (-pi/2, pi/2); tangent is strictly increasing on every branch and has range [-1, 1].

The period is pi; zeros are 0; vertical asymptotes are -pi/2, pi/2; defined branches are (-pi/2, pi/2); tangent is strictly increasing on every branch and has range (-infinity, infinity).

The choices are visible. Checking your work and seeing which answer is correct happen inside Gozunta.

Use the graph of \(y~=~\tan(x)\) on \((-\pi~/2,~\pi~/2)\) to state the period, all zeros, vertical asymptotes, defined branches, monotonicity on each branch, and range.

What this problem is really about

Turn the preview into practice.

Gozunta lets you study this problem—and more than 10,000 others.