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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.

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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.

enter image description here

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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.

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