Vertical Line Test :

A curve in the $\"xy-\"$ plane is the graph of a function of $\"x\"$ if and only if no vertical line intersects the curve more than once.

Observe the graph.

Draw a vertical line along the $\"y-\"$ axis, the line touches the curve only once.

The graph of the function passes the vertical line test.

Hence, by the definition of vertical line test, the graph is a function of $\"x\"$ .

The domain is the set of all values of $\"x\"$ on the curve.

The curve is defined for $\"-2\\leqslant$ .

The domain of the function is $\"\\left$ .

The range is the set of all values of $\"y\"$ on the curve.

The curve takes all the value from $\"-1\"$ to $\"2\"$ .

The range of the function is $\"\\left$ .

Yes, graph is a function of $\"x\"$ .

The domain and range of the function is $\"\\left$ and $\"\\left$ .