Math jan 13
.pdf
School
Fanshawe College**We aren't endorsed by this school
Course
MATH 1036
Subject
Mathematics
Date
Jan 13, 2025
Pages
8
Uploaded by CorporalMoonToad34
1. Analyse the following graph. Graph h(m) = -270 180 [-90 o | 90 KO/WO\%] 450 vw 720" r(°) Does it represent a periodic function? Justify your answer. Determine the period and amplitude if it is a periodic function.
2. Analyse the following graph. Graph y axis X axis Does it represent a periodic function? Justify your answer. Determine the period and amplitude if it is a periodic function.
3. Analyse the following graph. Graph (" A 2 1\5 1 0 > o 05 > 4 -3 -2 -1 0 2/ 3 4 5 6 8 9 -05 -4 A X axis Does it represent a periodic function? Justify your answer. Determine the period and amplitude if it is a periodic function.
Predict how the graph of this periodic function will be different than the one shown in Exercise 1. 4. Complete the following table of values: Suggested answers Rotation of wheel (degrees) Height, relative to X -axis (metres) 0° 90° 180° 270° 360° 450° 540° 630° 720° In your notebook, graph the points in the table. What is the resulting graph resemble? Was your prediction accurate? Explain. Determine the period for this new graph. In what situation would the period change for a Ferris wheel?
Assess your understanding: Y =sin x 5. A miniature Ferris wheel, with a diameter of 2 TN, is constructed for an advertisement display. It rotates once each minute. The following diagram represents the Ferris wheel relative to the Cartesian plane. Graph y axis D Press here for long description Determine the coordinates of the points A B C and .D on the diagram. Use the points you found earlier to complete the following table: Rotation of wheel (degrees) Height, relative to -axis (metres) 0° 90° 180° 270° 360° 450° 540° 630° 720°
In your notebook, graph the points in the table. Draw a curve of best fit through the points. Compare the graph you have drawn to the graph of Y =Sin . Whatdo you notice? State the period and the amplitude of the graph. Assess your understanding: Transformations 2 . 6. State the amplitude and the range of the graph of Y = 3 sSin x. ~ Amplitude + Range
7. State the amplitude and the range of the graph of Y = — 6 sin x. + Amplitude + Range Which of the previous represents a vertical stretch and a reflection in the &-axis of the graph of iy —S111 XL? Which of the previous represents a vertical compression of the graph of Yy =—S111 7 Create an equation in the form Y — Q@ SIN I that represents the following description: 3 The graph’s minimum Y-value is — 5 and the maximum v is < valiue IS 5 - Create an equation in the form Y — Q@ SIN I that represents the following description:
The range of the graph is R = {y c R| —04 < Yy < O.4}andthe graph is reflected in the Z-axis. Create an equation in the form Y = @ SIN T + Cfor: The graph of Y —SIN X after it is translated down five units. Create an equation in the form Y — Q@ sin —+ c for: The graph of Y —SIN X after it is reflected in the &- axis and shifted up six units. 8. Create an equationinthe fom Yy — Q@ sin (:1: — d) ~+ Cthat represents the given transformations of the graph of Y =—S111 L. The graph of Y =sin T is vertically stretched by 4 shifted 28 ° to the left, and translated three units up. The graph of Y —=SIN Z is shifted right 55 ° and up seven units.