MCF3M1
Date: ____________
Lesson 4 – More Transformations of Sinusoidal Functions
Yesterday we looked at the effect of horizontal and vertical translations on the graph of
f ( x)  sin x . Let’s look at the effect of a vertical stretch or compression.
1. Record the amplitude and equation of the axis for each sine curve shown.
a)
b)
y  3 sin x  2
y  4 sin x  1
2. What do you notice about the amplitude and equation of the axis, compared to the equation
of the function?
3. How does the amplitude affect the graph of the sin function?
Example 1
State the transformations that are applied to each sinusoidal function and state the range.
a) f ( x)  3 sin( x  35)  2
b) f ( x)  0.5 sin( x  90)  4
MCF3M1
Example 2
Write the equation of the sin function that has undergone the following translations.
a) Stetched by a factor of 4, shifted right 45o, shifted down 2 units.
b) Compressed by a factor of 0.3, reflected in the x-axis, shifted left 120o and up 4 units.
Example 3
Sketch the graph of f ( x)  2 sin( x  45)  1
Example 4
Determine the equation of the following graph.
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