Question

Use the graph below to answer the question that follows:

Answer 1

Answer:

The trignometric function that best represents the graph is:

$f(x)=4 \sin(x-\dfrac{\pi}{2})$

Step-by-step explanation:

It is given that the trignometric function passes through:

(0,-4) , (π/2,0) , (π,4) , (3π/2,0) , (2π,-4) and (5π/2,0) and (3π,4)

We will check these points in each of the given options and see what holds true.

2)

$f(x)=4\cos (x-\dfrac{\pi}{2})$

When we put x=0 we obtain:

$f(0)=4\cos (0-\dfrac{\pi}{2})\\\\f(0)=4\cos (-\dfrac{\pi}{2})\\\\f(0)=4\cos (\dfrac{\pi}{2})\\\\Since,\\\cos (-\theta)=\cos (\theta)\\\\Hence,\\f(0)=0\neq -4$

Hence, option 2 is incorrect.

3)

$f(x)=4 \sin(x-\dfrac{\pi}{2})+1$

When we put x=0 we get:

$f(0)=4 \sin (0-\dfrac{\pi}{2})+1\\\\f(0)=4 \sin (-\dfrac{\pi}{2})+1\\\\f(0)=-4\sin (\dfrac{\pi}{2})+1\\\\Since,\\\sin (-\theta)=\sin (\theta)\\Hence,\\f(0)=-4+1\\\\f(0)=-3\neq -4$

Hence, option 3 is incorrect.

4)

$f(x)=4\cos (x-\dfrac{\pi}{2})+1$

When we put x=0 we obtain:

$f(0)=4\cos (0-\dfrac{\pi}{2})+1\\\\f(0)=4\cos (-\dfrac{\pi}{2})+1\\\\f(0)=4\cos (\dfrac{\pi}{2})+1\\\\Since,\\\cos (-\theta)=\cos (\theta)\\\\Hence,\\f(0)=1\neq -4$

Hence, option 4 is incorrect.

1)

$f(x)=4 \sin(x-\dfrac{\pi}{2})$

When we put each of the x-value we see that the y-value also holds.

Hence, option 1 is true.

Also we can see in the graph.