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Give an equation of the form f(x) = A tan(Bx – C) + D which could be used to represent the given graph. (Note that C or D may be zero.) It It 4 -2 -3 a) O f(x)= -2 tan(x) +1 b) O f(x) = -2 tan(2x – 1) – 1 c) O f(x) = -2 tan(2x – T) +1 d) O f(x) = -2 tan(2x) e) O f(x) = -2 tan(2x – T) f) O None of the above.

Give an equation of the form f(x) = A tan(Bx – C) + D which could be used to represent the given graph. (Note that C or D may be zero.) It It 4 -2 -3 a) O f(x)= -2 tan(x) +1 b) O f(x) = -2 tan(2x – 1) – 1 c) O f(x) = -2 tan(2x – T) +1 d) O f(x) = -2 tan(2x) e) O f(x) = -2 tan(2x – T) f) O None of the above.

Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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i have trouble with tangent graphs. i wasnt able to answer this correctly. can someone explain to me how to do these. answer choices are in the image.

MUST BE DONE WITHOUT A CALCULATOR there is only one right answer

**Question:** Give an equation of the form \( f(x) = A \tan(Bx - C) + D \) which could be used to represent the given graph. (Note that C or D may be zero.) **Graph Explanation:** The graph shown is a series of tangent curves which are periodic and have vertical asymptotes. The vertical asymptotes occur at intervals, such as \(-\frac{\pi}{4}\), \(\frac{\pi}{4}\), \(\frac{3\pi}{4}\), and others symmetrically spaced. The curves are reflected and shifted upwards. **Possible Answers:** a) \( f(x) = -2 \tan(x) + 1 \) (Correct Answer) b) \( f(x) = -2 \tan(2x - \pi) - 1 \) c) \( f(x) = -2 \tan(2x - \pi) + 1 \) d) \( f(x) = -2 \tan(2x) \) e) \( f(x) = -2 \tan(2x - \pi) \) f) None of the above. The correct choice is option (a), where the equation for the graph is \( f(x) = -2 \tan(x) + 1 \). This equation correctly represents the vertical stretching, reflection, and vertical shift present in the graph.
Transcribed Image Text:**Question:** Give an equation of the form \( f(x) = A \tan(Bx - C) + D \) which could be used to represent the given graph. (Note that C or D may be zero.) **Graph Explanation:** The graph shown is a series of tangent curves which are periodic and have vertical asymptotes. The vertical asymptotes occur at intervals, such as \(-\frac{\pi}{4}\), \(\frac{\pi}{4}\), \(\frac{3\pi}{4}\), and others symmetrically spaced. The curves are reflected and shifted upwards. **Possible Answers:** a) \( f(x) = -2 \tan(x) + 1 \) (Correct Answer) b) \( f(x) = -2 \tan(2x - \pi) - 1 \) c) \( f(x) = -2 \tan(2x - \pi) + 1 \) d) \( f(x) = -2 \tan(2x) \) e) \( f(x) = -2 \tan(2x - \pi) \) f) None of the above. The correct choice is option (a), where the equation for the graph is \( f(x) = -2 \tan(x) + 1 \). This equation correctly represents the vertical stretching, reflection, and vertical shift present in the graph.
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