Question

The graph of which function passes through (0,3) and has an amplitude of 3? f (x) = sine (x) + 3 f (x) = cosine (x) + 3 f (x) = 3 sine (x) f (x) = 3 cosine (x)

Answer 1

D

Explanation:

edge

Answer 2

`f(x)=3*cosine(x)`

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
`f(x)=sin(x)`,
`f(0)= 0`; therefore the function we a looking for cannot be a sine function because it is zero at
`x=0`.

However, the cosine function
`f(x)=cos(x)` gives non-zero value at
`x=0:`

`f(0)=cos(0)=1`

therefore, a cosine function can be our function.

Now, cosine function with amplitude
`a` has the form

`f(x)=a*cos(x)`

this is because the cosine function is maximum at
`x= 0` and therefore, has the property that

`f(0)=a*cos(0)= a`

in other words it contains the point
`(0, a)`.

The function we are looking for contains the point
`(0, 3)`; therefore, its amplitude must be 3, or

`f(x)=3cos(x)`

we see that this function satisfies our conditions:
`f(x)` has amplitude of 3, and it passes through the point (0, 3) because
`f(0)=3`