How do you work out where construction lines go when sketching graphs such as f(x)=x sin x?

I am finding it difficult to understand how to calculate construction lines for graphs such as that given above.

Here, I know the lines are at y=abs(x) and y=-abs(x) but how do I work this out for myself?

1 Answer
Jan 10, 2018

When you graph any function of the form A(x)sinx we note that as x varies then sinx oscillates between +-1. As a result the graph of y=A(x)sinx will be sinusoidal and oscillate between +-A(x) (the amplitude).

The same principle applies equally other periodic functions,

Thus if we want to graph y=sinx we first start with separate sketches of y=sinx
graph{sinx [-15, 15, -10, 10]}

And y=+-x:
graph{(y-x)(y+x)=0 [-15, 15, -10, 10]}

We can now sketch the oscillations so that they lie between the A(x) function:
graph{(y-x)(y+x)(y-xsinx)=0 [-15, 15, -10, 10]}

Leading to the final graph
graph{xsinx [-15, 15, -10, 10]}