Answer:
[tex]f(x)=3*cosine(x)[/tex]
Step-by-step explanation:
We are looking for a trigonometric function which contains the point (0, 3), and has an amplitude of 3.
We know that for a sine function [tex]f(x)=sin(x)[/tex], [tex]f(0)= 0[/tex]; therefore the function we a looking for cannot be a sine function because it is zero at [tex]x=0[/tex].
However, the cosine function [tex]f(x)=cos(x)[/tex] gives non-zero value at [tex]x=0:[/tex]
[tex]f(0)=cos(0)=1[/tex]
therefore, a cosine function can be our function.
Now, cosine function with amplitude [tex]a[/tex] has the form
[tex]f(x)=a*cos(x)[/tex]
this is because the cosine function is maximum at [tex]x= 0[/tex] and therefore, has the property that
[tex]f(0)=a*cos(0)= a[/tex]
in other words it contains the point [tex](0, a)[/tex].
The function we are looking for contains the point [tex](0, 3)[/tex]; therefore, its amplitude must be 3, or
[tex]f(x)=3cos(x)[/tex]
we see that this function satisfies our conditions: [tex]f(x)[/tex] has amplitude of 3, and it passes through the point (0, 3) because [tex]f(0)=3[/tex]
