What will be it's graph?

Question

What will be the graph of $y=2x +\sin x $ and $y=x \sin x$ and what's the method to graph functions of this type.

Answer 1

Simply make a value table to draw the graph.

Neither do the given graphs have a special name, nor is there a special method to draw the graphs.

Answer 2

Let's do the first function $f(x)=2x+\sin(x)$. We can see that:

• $D_f=\mathbb R$.

• The function is differentiable in $\mathbb R$.

• $f'(x)=2+\cos(x)$. Since $|\cos(x)|\leq1$ so $f'(x)\subseteq [+1,+3]$ so for all $x\in D_f$, $f'>0$ so $f(x)$ is always increasing.

By a nice table of $x$ and their $y$'s we have the following plot. I made it using Maple.