The comparison between the standard form of the cosine and f(x)=34cos(3x)+4 shows that the amplitude of the function given is 34.
Cosine Functions
The standard form of the cosine is given by:
y=acos(bx+c)+d
where:
a= amplitude - half the distance between the maximum and minimum values of the function. The value of a will be |a|.
b= the number of cycles the function completes in an interval of from 0 to 2π. This parameter influences in the period since is [tex]\frac{2\pi }{b}[/tex].
c= horizontal shift
d= vertical shift
The question asks the value of amplitude. Therefore, you should compare the standard form with equation function given.
Thus, you have:
y=acos(bx+c)+d
f(x)=34cos(3x)+4
The comparison shows: a=34, b=3, c=0 and d=4
Hence, the amplitude of the function f(x)=34cos(3x)+4 is equal to 34.
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