Answer
$$
f(x)=\frac{x}{2 x^{2}+x}
$$
is continuous for all real numbers $x$ except $x = 0$ , $ x = -\frac{1}{2}$.
Work Step by Step
$$
f(x)=\frac{x}{2 x^{2}+x}
$$
The function being graphed is a rational function, and hence is continuous at every number where the denominator is nonzero.
Solving the equation
$$
2 x^{2}+x=x(2x+1)=0
$$
yields discontinuities at $x = 0$ and at $ x = -\frac{1}{2}$.
Therefore the function
$$
f(x)=\frac{x}{2 x^{2}+x}
$$
is continuous for all real numbers $x$ except $x = 0$ , $ x = -\frac{1}{2}$
