Question

in the graph in red is y=3 sin(x) what would the graph in blue be ?

Answer 1

Here the blue graph seems as reverse function of the red graph, but not having the same range. So the blue graph is a negative graph.

Since the red graph is  y = 3 sin(x),  its range will be the interval [-3, 3].

We can see that the range of the blue graph is lesser than that of the red graph. So we can just say that the range of the blue graph is [-n, n], where n ∈ (0, 3).

So the blue graph will be in the form  y = - n sin(x),  where n ∈ (0, 3),  as we mentioned above.

The minus sign in the equation is that the graph goes oppositely for the red graph. Since sign of red graph is '+', then that of blue graph will be '-'.

Here the numbers are not represented in the axes, so we can't guarantee a unique value for 'n'. If there were numbers, then we could. That's a problem here.

E.g., if the point at the y - axis near the crest of the blue graph was given (0, 2), or if the point at the y - axis near the trough of the blue graph was given (0, -2), then we could say that the graph is  y = -2 sin(x). Here  n = 2  and the range of the graph will be [-2, 2].