Restricting The Domain Of A Parabola

If you want the inverse of a parabola to be a function you will need to restrict the domain. If you don t restrict the domain the inverse of a parabola will look like. We can see this is a parabola with vertex at latex left 2 3 right latex that opens upward.

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If you have a parabola with name c then c is the implicit equation of parabola then you can write rightside c if 1 x 2 0 leftside c in input bar for limiting the graph last trick was wrote by an user in the last mounth but i do not remember in what topic.

Restricting the domain of a parabola. And this does not represent a function of x. If you had only the top half in red or the bottom half in blue they would each be a function of x. The if comand limit the domain.

An implicit function can be limited y x if 1 x 2 0. In this tutorial we look at how to find the inverse of a parabola and more importantly how to restrict the domain so that the inverse is a function. Parabola informally a restriction of a function is the result of trimming its domain.

Because the graph will be decreasing on one side of the vertex and increasing on the other side we can restrict this function to a domain on which it will be one to one by limiting the domain to latex x ge 2 latex.