Complete Answers to Trigonometric Function Graph Questions

The detailed answers below correspond to the questions presented in Graphs of Trigonometric Functions - Questions.

Graph Identification Answers

Question 1: Cosine Function

Function: \( f(x) = \cos x \)

Correct Graph: d

Question 2: Cotangent Function

Function: \( f(x) = \cot x \)

Correct Graph: d

Question 3: Cosine with Negative Argument

Function: \( f(x) = \cos (-x) \)

Correct Graph: d

Question 4: Horizontal Shift of Cosine

Function: \( f(x) = \cos \left(x - \frac{\pi}{4}\right) \)

Correct Graph: a

Question 5: Transformed Cosecant Function

Function: \( f(x) = -\csc \left(x + \frac{\pi}{4}\right) \)

Correct Graph: a

Question 6: Reflected and Shifted Cosine

Function: \( f(x) = -\cos \left(x - \frac{\pi}{4}\right) \)

Correct Graph: b

Question 7: Vertically Stretched Tangent

Function: \( f(x) = -2 \tan x \)

Correct Graph: a

Question 8: Complex Sine Transformation

Function: \( f(x) = -\sin \left(-x - \frac{\pi}{4}\right) \)

Correct Graph: a

Question 9: Scaled and Reflected Secant

Function: \( f(x) = 2 \sec (-2x) \)

Correct Graph: c

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