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M3-035-A05-V04
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F-TF.2.1
Warmup
M3-035-A05-V04
Graph all six basic trigonometric functions.
Specify secant asymptotes and reciprocal-branch vertices
Problem
Use the graph of \(y~=~\sec(x)\) on \([-2\pi~,~0]\) to state the period, parity, all vertical asymptotes, upward-branch minima, downward-branch maxima, zeros, and range.
Answer choices
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A
The period is 2pi and secant is even. Vertical asymptotes are -3pi/2, -pi/2; upward-branch minima are (-2pi, 1), (0, 1); downward-branch maxima are (-pi, -1); there are no zeros; and the range is (-infinity, infinity).
B
The period is 2pi and secant is odd. Vertical asymptotes are -3pi/2, -pi/2; upward-branch minima are (-2pi, 1), (0, 1); downward-branch maxima are (-pi, -1); there are no zeros; and the range is (-infinity, -1] union [1, infinity).
C
The period is 2pi and secant is even. Vertical asymptotes are -3pi/2, -pi/2; upward-branch minima are (-2pi, 1), (0, 1); downward-branch maxima are (-pi, -1); there are no zeros; and the range is (-infinity, -1] union [1, infinity).
D
The period is pi and secant is even. Vertical asymptotes are -3pi/2, -pi/2; upward-branch minima are (-2pi, 1), (0, 1); downward-branch maxima are (-pi, -1); there are no zeros; and the range is (-infinity, -1] union [1, infinity).
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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 secant asymptotes and reciprocal-branch vertices
