It is required to draw the graph of -3f(x), where f(x)=cos x.
It is also required to give its period.
To do this, start with the graph of the parent function f(x)=cos x, then perform transformations on the graph of the parent function to draw the required graph.
The graph of the parent function f(x)=cos x is shown below:
Reflect the graph over the x-axis to draw the graph of -f(x) (in blue):
Stretch the graph of -f(x) vertically by a factor of 3 to draw the graph of -3f(x) (in green):
The required graph of -3f(x) is:
Recall that the period of a sinusoid is the length of a complete cycle.
From the graph, the period is 2π.
