Unit 6, Lesson 15
Transforming Trigonometric Functions
Integrated Math 3
15.1
Warm-up
Translated Parabolas
Match each equation with its graph. Be prepared to explain your reasoning.
A
B
C
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Match each equation with its graph. Be prepared to explain your reasoning.
A
B
C
A fan has a radius of 1 foot. A point,
Sketch a graph of the horizontal position,
Sketch a graph of the vertical position,
The graphs of cosine and sine functions can be translated vertically or horizontally, and the size or height of their graphs can also be modified similarly to how we transformed other types of functions in an earlier unit. Let’s look at the graphs of
The coefficient 2 stretches the graph vertically, doubling the amplitude of the sine graph. This means that the distance from the midline to the maximum or minimum value is now 2 instead of 1. Adding 3 to the equation translates the midline up by 3 units.
What if we want to translate the graph of