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Part 1
Use the method of adding​ y-coordinates to graph the function.
f left parenthesis x right parenthesis equals cosine left parenthesis 2 x right parenthesis minus sine left parenthesis 2 x right parenthesis
Question content area bottom
Part 1
Choose the correct graph of the function.
A.
-2
-1
1
2
x
y
piStartFraction pi Over 2 EndFraction

A coordinate system has a horizontal x-axis labeled from negative StartFraction pi over 2 End Fraction to StartFraction 3 pi over 2 End Fraction in increments of StartFraction pi over 4 End Fraction and a vertical y-axis labeled from negative 2.5 to 2.5 in increments of 1. Upper A repeating curve with a period of pi fills the graph. Within one period comma the curve starts at left parenthesis negative StartFraction pi over 8 EndFraction comma 0 right parenthesis comma rises to a maximum at left parenthesis StartFraction pi over 8 EndFraction comma 1.4 right parenthesis comma falls comma passing through left parenthesis StartFraction 3 pi over 8 EndFraction comma 0 right parenthesis comma to a minimum at left parenthesis StartFraction 5 pi over 8 EndFraction comma negative 1.4 right parenthesis and rises to the point left parenthesis StartFraction 7 pi over 8 EndFraction comma 0 right parenthesis. All coordinates are approximate.
B.
-2
-1
1
2
x
y
piStartFraction pi Over 2 EndFraction

A coordinate system has a horizontal x-axis labeled from negative StartFraction pi over 2 End Fraction to StartFraction 3 pi over 2 End Fraction in increments of StartFraction pi over 4 End Fraction and a vertical y-axis labeled from negative 2.5 to 2.5 in increments of 1. Upper A repeating curve with a period of pi fills the graph. Within one period comma the curve starts at left parenthesis negative StartFraction pi over 8 EndFraction comma 1.4 right parenthesis comma falls comma passing through the point left parenthesis StartFraction pi over 8 comma 0 right parenthesis comma to a minimum at left parenthesis StartFraction 3 pi over 8 EndFraction comma negative 1.4 right parenthesis comma and rises comma passing through left parenthesis StartFraction 5 pi over 8 comma 0 right parenthesis comma to a maximum at left parenthesis StartFraction 7 pi over 8 EndFraction comma 1.4 right parenthesis. All coordinates are approximate.
C.
-2
-1
1
2
x
y
piStartFraction pi Over 2 EndFraction

A coordinate system has a horizontal x-axis labeled from negative StartFraction pi over 2 End Fraction to StartFraction 3 pi over 2 End Fraction in increments of StartFraction pi over 4 End Fraction and a vertical y-axis labeled from negative 2.5 to 2.5 in increments of 1. Upper A repeating curve with a period of pi fills the graph. Within one period comma the curve starts at left parenthesis 0 comma 2 right parenthesis comma falls comma passing through left parenthesis StartFraction pi over 4 EndFraction comma 0 right parenthesis comma to a minimum at left parenthesis StartFraction pi over 2 EndFraction comma negative 2 right parenthesis comma and rises comma passing through the point left parenthesis StartFraction 3 pi over 4 EndFraction comma 0 right parenthesis comma to the point left parenthesis pi comma 2 right parenthesis. All coordinates are approximate.
D.
-2
-1
1
2
x
y
piStartFraction pi Over 2 EndFraction

The correct graph of the function is A. The curve on graph A starts at a maximum, falls to a minimum, and then rises back to a maximum within one period, which matches the description of the function f(x) = cos(2x) - sin(2x).