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ACTIVITY 14.2
Developing Concepts
GROUP ACTIVITY
Group Activity for use with Lesson 14.2
Translating and
Reflecting Trigonometric Graphs
QUESTION
How can you graph reflections and horizontal and vertical
translations of graphs of trigonometric functions?
Work with a partner.
MATERIALS
graphing calculator
EXPLORING THE CONCEPT
1 Use a graphing calculator to graph each pair of functions in the same viewing
window. How are the graphs geometrically related?
a. y = cos x
3
c. y = sin 3x
5
3
y = º sin 3x
5
b. y = 2 sin x
y = ºcos x
y = º2 sin x
2 Use a graphing calculator to graph each pair of functions in the same viewing
window. How are the graphs geometrically related?
a. y = cos x
b. y = 2 sin x
y = cos x º π
2
c. y = sin 3x
y = 2 sin x + π
2
y = sin 3(x + π)
3 Use a graphing calculator to graph each pair of functions in the same viewing
window. How are the graphs geometrically related?
a. y = cos x
1
c. y = sin 3x
4
1
y = 4 sin 3x º 2
b. y = 2 sin x
y = cos x + 1
y = 2 sin x º 1
DRAWING CONCLUSIONS
1. Predict what the graph of each function looks like by making a sketch. Check
your prediction by graphing the function on a graphing calculator.
a. y = º3 cos x
3π
b. y = sin x + 4
c. y = sin x º 4
2. Predict what the graph of each function looks like by making a sketch. Check
your prediction by graphing the function on a graphing calculator.
1
a. y = º cos x º 2
2
b. y = º3 cos (x + π)
c. y = 2 sin (x º π) + 3
π
d. y = º4 sin x º º 6
4
3. CRITICAL THINKING Use the following phrases to describe how the graph of
each function in parts (a)–(d) is related to the graph of y = sin x.
•
•
•
shifted up 1 unit
shifted left 1 unit
•
•
shifted down 1 unit
shifted right 1 unit
reflected in a horizontal line
a. y = sin (x º 1) + 1
b. y = ºsin (x º 1) º 1
c. y = ºsin (x + 1) + 1
d. y = sin (x + 1) º 1
14.2 Concept Activity
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