Question

Please Help Me

Answer 1

What can you say about their amplitudes

Answer 2

Or their frequencies? Are they the same? Are they shifted?

Answer 3

Their frequencies have shifted, but I'm not sure about the amplitudes

Answer 4

have you covered function transformations? like for say a quadratic function or a linear one?

Answer 5

f(x) = 2cos(pi*x); g(x) = 2cos(2*pi*x)
Amplitude for both is 2.
Period of f(x) = 2pi/pi = 2. Period of g(x) = 2pi/(2pi) = 1
g(x) can be obtained from f(x) by replacing x by 2x. Whenever, x is multiplied by a factor greater than 1, the graph will be compressed horizontally by that factor.

Answer 6

2) y = -3tan(x/2).

Period: Since tan(x) has a period of pi, tan(x/2) will have a period of pi / (1/2) = 2(pi).

Domain: tan(x) is undefined when x is: pi/2 + n(pi) where n is an integer ...-2, -1, 0, 1, 2, .... Therefore tan(x/2) will be undefined when x is: pi + 2n(pi) or (2n+1)pi. Domain of tan(x/2) is:

\[{x|x≠(2n+1)π,n=...,−2,−1,0,1,...}=
{x|x≠...,−3π,−π,π,3π,...}\]


Range: tan(x) has the range (-infinity, infinity) and so does tan(x/2)

Zeros: tan(x) has zeros at x = n(pi) where n is an integer: ...-1, 0, 1, ...
Therefore, tan(x/2) has zeros at x = 2n(pi) where n is an integer: ...-1, 0, 1, ... or at x = ..., -4pi, -2pi, 0, 2pi, 4pi, ...

Asymptotes: Vertical asymptotes will be when tan(x/2) goes to +/- infinity. We found those point earlier and excluded them from the domain because tan(x/2) will be undefined at those x values. Those same x values will be the location of the vertical asymptotes. At x = (2n+1)pi where n is an integer ot at x = ..., -3pi, -pi, pi, 3pi, ...

Answer 7

3) Amplitude and period of y = -sin (x - pi/4) + 2
In y = Asin(Bx + C) + D
lAl is the amplitude
B is the horizontal stretch/shrink factor. We can also calculate the period of the function from B. Period = 2(pi)/B
C/B is the phase shift. If C/B is negative, the shift is to the right. If C/B is positive, the shift is to the left.
D is the vertical shift. If D is positive, the graph shifts upward. If D is negative, the graph shifts downward.

Here A = -1. Amplitude is |A| = l-1l = 1.
Period = 2(pi)/B = 2(pi)/1 = 2(pi).

Answer 8

Sorry do i need to take it down a notch or do you understand ?

Answer 9

@ohohaye

Answer 10

@optiquest can you understand my work? i need you opinion if not then i need to rephrase so that you and her can understand a little clearer : )

Answer 11

Yeah makes sense to me

Answer 12

BTW: "Their frequencies have shifted, but I'm not sure about the amplitudes"

The frequencies are not shifted - this happens when you add or subtract with the function, you multiplied the phase which stretches or compacts the sine wave

Answer 13

Cos in this case

Answer 14

Shift means you move the entire thing left/right/up/down

Answer 15

Yes

Answer 16

similar to y=mx+b, b would be your shift up or down