a Transform the parent function, y=sin x, until it has the desired period and horizontal translation.
B
b Transform the parent function, y=sin x, until it has the desired period, amplitude, and vertical translation.
C
c Transform the parent function, y=cos x, until it has the desired amplitude, and horizontal translation.
D
d Transform the parent function, y=cos x, until it has the desired period and horizontal translation.
A
aDiagram:
B
bDiagram:
C
cDiagram:
D
dDiagram:
Practice makes perfect
a Let's have a look at the general equation for a sine curve.
y&= asin[ b(x- h)]+k [0.5em]
a&=amplitude
b&=period
h&=horizontal translation
k&=vertical translationExamining the given equation, we notice that the sine curve has a period that is twice the length of its parent function, y=sin x. Since the parent function has a period of 2Ï€, the given function must have a period of 4Ï€.
Finally, we have to translate the function to the right by π units.
b Examining the equation, we see that it has an amplitude of 10. Let's start by showing this transformation.
Finally, we have to vertically translate the curve by 2 units in the negative direction.
c Let's have a look at the general equation for a cosine curve.
y&= acos[ b(x- h)]+k [0.5em]
a&=amplitude
b&=period
h&=horizontal translation
k&=vertical translationExamining the equation, we see that it has an amplitude of 5. Let's start by showing this transformation.
Finally, we have to horizontally translate the graph to the left by π4 units.
d Examining the given equation, we notice that the cosine curve has a period that is half that of its parent function, y=cos x. Since the parent function has a period of 2π, the given function must have a period of π.
Finally, we have to translate the function to the right by π4 units.
