The parabola in the image can handle any real number you throw at it! Its domain, the set of all possible inputs, is all real numbers. No matter what real number you plug in, it will always output a valid real number back.
The graph you showed me represents a parabola, and a cool thing about parabolas is that they can handle any real number you throw at them! Their domain, which is the set of all possible input values, encompasses all real numbers. This means no matter what real number you plug into the function, it will always give you a valid real number back as the output.
There are a few reasons for this:
Parabolas are defined by an equation like y = x^2 + k, where k is any real number. Solving this equation for x always gives you a real number output for any real number y you put in.
Parabolas are continuous, meaning small changes in the input lead to small changes in the output. No weird jumps or gaps!
They're symmetrical around their "axis of symmetry," so for any input x, you'll also get a valid output of -y.