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M3-035-A06-V04
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F-TF.2.1
Warmup
M3-035-A06-V04
Graph all six basic trigonometric functions.
Specify cotangent zeros, asymptotes, and decreasing branches
Problem
Use the graph of \(y~=~\cot(x)\) on \((-\pi~,~0)\) to state the period, all zeros, vertical asymptotes, defined branches, monotonic direction and end behavior on each full branch, and range.
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A
The period is pi; zeros are (-pi/2, 0); vertical asymptotes are -pi, 0; defined branches are (-pi, 0); cotangent is strictly decreasing from positive infinity to negative infinity on each full branch, and its range is [-1, 1].
B
The period is pi; zeros are (-pi/2, 0); vertical asymptotes are -pi, 0; defined branches are (-pi, 0); cotangent is strictly increasing from positive infinity to negative infinity on each full branch, and its range is all real numbers.
C
The period is pi; zeros are (-pi/2, 0); vertical asymptotes are -pi, 0; defined branches are (-pi, 0); cotangent is strictly decreasing from positive infinity to negative infinity on each full branch, and its range is all real numbers.
D
The period is 2pi; zeros are (-pi/2, 0); vertical asymptotes are -pi, 0; defined branches are (-pi, 0); cotangent is strictly decreasing from positive infinity to negative infinity on each full branch, and its range is all real numbers.
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Curriculum context
Standard F-TF.2.1
Category Functions
Domain Trigonometric Functions
Objective Graph all six basic trigonometric functions.
Problem type Specify cotangent zeros, asymptotes, and decreasing branches
