a The function has a different period than its parent function, y=sin x.
B
b The function has a different period and amplitude than its parent function, y=sin x.
C
c The function has a different period, amplitude, and vertical position than its parent function, y=sin x.
A
aDiagram:
B
bDiagram:
C
cDiagram:
Practice makes perfect
a Let's have a look at the general equation for a sine function.
y&= asin[ b(x- h)]+k [0.5em]
a&=amplitude
b&=period
h&=horizontal translation
k&=vertical translation
If we compare the given equation with its parent function, y=sin x, we notice that x has a coefficient of 2Ď€. This changes the curve's period according to the following formula.
Period=2Ď€/b
Let's substitute the value of b in the formula and simplify.
The function has a period of 1. Now we can graph the function.
b Again, if we compare the given function to its parent function we see that it has a different amplitude and period.
y= 3sin π x
The amplitude is given by the coefficient to sin(Ď€ x), which is 3. This means we have to stretch the function until the vertical distance between the midline and the function's peaks and troughs is 3.
To determine the function's period, we will use the same formula as in Part A.
The function has a period of 2. Now we have all the information we need to graph it.
c Similar to Parts A and B, by examining the equation we can see that it has a period of 1 and an amplitude of 2. We can also identify a vertical translation of 1 compared to the parent function.
y= 2sin 2Ď€ x+1
With this information, we can draw the graph.
