Graphs are used to represent functions and relations.
- The function shown on the graph is f(x) = -1/2 sin(x)
- See attachment for the graph of g(x) = 4 cos(x)
How to determine the function of the graph
From the graph, we have the following ordered pairs
[tex](x,y) = (\pi,0)[/tex]
[tex](x,y) = (2\pi,0)[/tex]
The above ordered pairs show that the graph is a sine function.
So, let the function be represented as:
[tex]y = a\sin(x)[/tex]
From the graph, we have the following ordered pair
[tex](x,y) = (\pi/2,-1/2)[/tex]
So, we have:
[tex]-\frac 12 = a * \sin(\pi/2)[/tex]
This gives
[tex]-\frac 12 = a * 1\\[/tex]
Evaluate the product
[tex]-\frac 12 = a[/tex]
Rewrite as:
[tex]a = -\frac 12[/tex]
Substitute -1/2 for a in [tex]y = a\sin(x)[/tex]
[tex]y = -\frac 12 \sin(x)[/tex]
Hence, the equation of the shown on the graph is [tex]f(x) = -\frac 12 \sin(x)[/tex]
See attachment for the graph of g(x) = 4 cos(x)
Read more about sine and cosine graphs at:
https://brainly.com/question/14290164
