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

Answer:

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

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 $f(x)=sin(x)$, $f(0)= 0$; 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 $f(0)=3$

Answer 2

Answer:

The answer is D on EDG

Step-by-step explanation: