Question

Find a, b and c for the function f(x) = a sin (bx - c) such that the graph of f  match the figure.

Answer 1

Step 1 :

The graph of the function is in the form of ,

where  is amplitude,  is the period and  is the shift along the - axis.

Step 2 :

Observe the graph.

The difference between the maximum height and the minimum height is twice of the amplitude of the function.

The amplitude of the function is .

From the graph, the sine curve starts downwards from the origin.

Thus, the amplitude of the function is .

Step 3 :

Period of the function is .

The sine function completes one half of the cycle between the times at maximum height and minimum height.

Then Period of the function is .

Step 4 :

 is the shift along the - axis.

Observe the graph of the function, there is no shift along the - axis.

.

Thus, the values of , , and .

Solution :

The values of , , and .