Question

need help plz Describe the transition between f(x)=3cos2x-1 and f(x)=-cos x/2+3

Answer 1

the graph for the equations

Answer 2

Okay we'll start from the left side to the right
General equation \(acos(bx-c)+d\)

\(3cos2x-1\)
\(-cos~\frac{x}{2}+3\)

Do you know what the a value controls?

Answer 3

the value controls the size of the cos equation

Answer 4

Yes sort of
It controls its vertical stretch and shrink

if a > 1, then its a stretch
If 0<a<1, then its a shrink

If a<0, then it was reflected across the x-axis

Answer 5

ok so i just say that it reflected across the x-axis b/c its describing the translation

Answer 6

Right and you also did a scale factor of 1/3 to the first equation to get to the second

\((3cos2x-1)\color{red}{\times \frac13}=>(cos2x-1)\color{red}{\times -1}=>-cos2x-1\)

Okay, now lets look at the b value
\(acos(bx-c)+d\)
Do you know what it controls?

Answer 7

it controls the hight and length basically?

Answer 8

Sort of again
In trig it works more as a change in the period of the function (Visually, its stretch or shrink)

So the b value tells you about its period (How long it takes for the equation to return to its same place)

If b>1 its period is smaller (The 'waves' are more closer to each other)
If 0<b<1 the period increases (The 'waves' are further from each other)

If b<0 there is a reflection across the y=axis

Answer 9

Am going to also add to my original statements about the a value

a indicates the amplitude (The length of the wave)
[Again the larger the value, the larger the wave height]

Answer 10

If the general equation is \(f(x) = a \cos(bx-c) + d\) is the general equation of the cosine function, then we should first clarify which values are \(c\) and which are \(d\), otherwise we might confuse the functions and get different graphs other than what we intended like this: https://www.geogebra.org/classic/unjeannc

Answer 11

i'm pretty sure its like Hero said with the equation