Answer:
The trignometric function that best represents the graph is:
[tex]f(x)=4 \sin(x-\dfrac{\pi}{2})[/tex]
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)
[tex]f(x)=4\cos (x-\dfrac{\pi}{2})[/tex]
When we put x=0 we obtain:
[tex]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[/tex]
Hence, option 2 is incorrect.
3)
[tex]f(x)=4 \sin(x-\dfrac{\pi}{2})+1[/tex]
When we put x=0 we get:
[tex]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[/tex]
Hence, option 3 is incorrect.
4)
[tex]f(x)=4\cos (x-\dfrac{\pi}{2})+1[/tex]
When we put x=0 we obtain:
[tex]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[/tex]
Hence, option 4 is incorrect.
1)
[tex]f(x)=4 \sin(x-\dfrac{\pi}{2})[/tex]
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.
The correct choice that shows the trigonometric function is;
Option B: f(x) = -4 cos(x - π/2)
From the given points of the graph, i have drawn the graph as seen in the attached file.
The given graph points correspond to those of a vertically stretched cosine function that has been shifted π/2 to the right and reflected across the x-axis. Therefore, the correct choice that shows the trigonometric function is;
Option B: f(x) = -4 cos(x - π/2)
Read more about Trigonometric Graphs at; https://brainly.com/question/27767092
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