Question

which function is graphed below?

Answer 1

Answer:

which one was it

Step-by-step explanation:

Answer 2

Answer:

The correct option is C. The given graph represents the function f(x)=sin(x).

Step-by-step explanation:

From the given graph it is clear that the initial value of the function is 0.

The maximum value of function is 1 at $x=\frac{\pi}{2}$.

The minimum value of function is -1 at $x=\frac{3\pi}{2}$.

The period of the function is 2π.

The x-intercepts are 0, π, 2π.

These are the properties of a positive sine function. The given graph represents the function f(x)=sin(x).

Therefore the correct option is C.

To confirm the solution find the value of each function at x=0, and $x=\frac{\pi}{2}$. The function must be satisfy by the points (0,0) and $(\frac{\pi}{2},1)$

For option (1),

$f(x)=-\cosx$

$f(0)=-\cos(0)=-1\neq 0$

Therefore option 1 is incorrect.

For option (2),

$f(x)=\cosx$

$f(0)=\cos(0)=1\neq 0$

Therefore option 2 is incorrect.

For option (3),

$f(x)=\sinx$

$f(0)=\sin(0)=0$

$f(\frac{\pi}{2})=\sin(\frac{\pi}{2})=1$

Therefore option 3 is correct.

For option (4),

$f(x)=-\sinx$

$f(0)=-\sin(0)=0$

$f(\frac{\pi}{2})=-\sin(\frac{\pi}{2})=-1\neq 1$

Therefore option 4 is incorrect.