Domanda del libro di testo
Match each function with its graph in choices A–I. (One choice will not be used.)
y = sin (x - π/4)
A. <IMAGE> B. <IMAGE> C. <IMAGE>
D. <IMAGE> E. <IMAGE> F. <IMAGE>
G. <IMAGE> H. <IMAGE> I. <IMAGE>
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Ch. 4 - Graphs of the Circular Functions
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891
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TOC.tableOfContents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Capitolo 5, Problema 9
Match each function with its graph in choices A–F.
y = tan (x - π )
A. <IMAGE> B. <IMAGE> C. <IMAGE>
D. <IMAGE> E. <IMAGE> F. <IMAGE>
Guida verificata passo dopo passo1
Recall the general shape and properties of the tangent function \(y = \tan x\), including its period \(\pi\), vertical asymptotes at \(x = \frac{\pi}{2} + k\pi\) for integers \(k\), and zeros at \(x = k\pi\).
Understand that the function \(y = \tan(x - \pi)\) represents a horizontal shift of the basic tangent function to the right by \(\pi\) units.
Determine the new locations of the vertical asymptotes and zeros after the shift: vertical asymptotes occur where \(x - \pi = \frac{\pi}{2} + k\pi\), so \(x = \frac{\pi}{2} + \pi + k\pi = \frac{3\pi}{2} + k\pi\), and zeros occur where \(x - \pi = k\pi\), so \(x = \pi + k\pi\).
Compare these shifted features (asymptotes and zeros) with the graphs in choices A–F to identify which graph matches the function \(y = \tan(x - \pi)\).
Confirm that the shape and orientation of the graph correspond to the tangent function's increasing behavior between asymptotes and that the period remains \(\pi\).
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Concetti chiave
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Properties of the Tangent Function
The tangent function, tan(x), is periodic with period π and has vertical asymptotes where cos(x) = 0, at x = ±π/2, ±3π/2, etc. Its graph repeats every π units and passes through the origin with increasing values between asymptotes. Understanding these properties helps identify the shape and key features of tan(x) graphs.
Video consigliato:
Percorso guidato
5:43
Introduction to Tangent Graph
Horizontal Phase Shift in Trigonometric Functions
A horizontal phase shift occurs when the input variable x is replaced by (x - c), shifting the graph c units to the right. For y = tan(x - π), the entire tangent graph shifts π units right, moving asymptotes and intercepts accordingly. Recognizing phase shifts is essential for matching transformed graphs to their functions.
Video consigliato:
Percorso guidato
6:31Phase Shifts
Identifying Graphs of Trigonometric Functions
Matching a trigonometric function to its graph requires analyzing key features like period, amplitude (if applicable), asymptotes, intercepts, and shifts. For tangent functions, focus on vertical asymptotes and zero crossings. Comparing these features with given graphs allows accurate identification of the correct match.
Video consigliato:
Percorso guidato
6:04Introduction to Trigonometric Functions
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