Domanda del libro di testo
For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = 2 sin 5x
688
views
Ch. 4 - Graphs of the Circular Functions
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
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–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>
Guida verificata passo dopo passo1
Recall that the function given is \(y = \sin\left(x - \frac{\pi}{4}\right)\), which represents a horizontal shift of the basic sine function \(y = \sin x\).
Understand that the expression \(x - \frac{\pi}{4}\) inside the sine function means the graph of \(y = \sin x\) is shifted to the right by \(\frac{\pi}{4}\) units.
Identify key points on the basic sine curve, such as zeros at multiples of \(\pi\), maximum at \(\frac{\pi}{2}\), and minimum at \(\frac{3\pi}{2}\), then shift all these points to the right by \(\frac{\pi}{4}\) to predict the shape of the graph for \(y = \sin\left(x - \frac{\pi}{4}\right)\).
Compare the predicted shifted sine wave with each graph option (A through I), looking for the graph that matches the rightward shift by \(\frac{\pi}{4}\) without any changes in amplitude or period.
Select the graph that correctly shows the sine wave shifted right by \(\frac{\pi}{4}\) and ignore the one choice that does not correspond to any function given.
Risposta video verificata per un problema simile:
Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Concetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Sine Function and Its Properties
The sine function, sin(x), is a periodic wave with amplitude 1, period 2π, and zero crossings at multiples of π. Understanding its shape, maximum and minimum values, and where it crosses the x-axis is essential for identifying its graph.
Video consigliato:
Percorso guidato
5:53
Graph of Sine and Cosine Function
Phase Shift in Trigonometric Functions
A phase shift occurs when the input variable x is replaced by (x - c), shifting the graph horizontally by c units. For y = sin(x - π/4), the sine wave shifts π/4 units to the right, altering the position of peaks, troughs, and zeros without changing amplitude or period.
Video consigliato:
Percorso guidato
6:31Phase Shifts
Graph Matching Techniques
Matching a function to its graph involves analyzing key features like amplitude, period, phase shift, and intercepts. Recognizing how transformations affect the graph helps eliminate incorrect options and identify the correct match among multiple choices.
Video consigliato:
Percorso guidato
4:08Graphing Intercepts
Pratica correlata
Domanda del libro di testo
For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = 1 + 2 sin ¼ x
588
views
Domanda del libro di testo
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>
691
views
Domanda del libro di testo
Fill in the blank(s) to correctly complete each sentence.
The graph of y = 3 + 5 cos (x + π/5) is obtained by shifting the graph of y = cos x horizontally ________ unit(s) to the __________, (right/left) stretching it vertically by a factor of ________, and then shifting it vertically ________ unit(s) __________. (up/down)
883
views
Domanda del libro di testo
Fill in the blank(s) to correctly complete each sentence.
The graph of y = -2 + 3 cos (x - π/6) is obtained by shifting the graph of y = cos x horizontally ________ unit(s) to the __________, (right/left) stretching it vertically by a factor of ________, and then shifting it vertically ________ unit(s) __________. (up/down)
666
views
Domanda del libro di testo
For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = 3 - ¼ cos ⅔ x
618
views