Mathematics: Why does the graph of a square root function look like half a parabola?

Why does the graph of a square root function look

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mytime8774

29.07.2019

Square root is the inverse of squaring something.a basic parabola $y=x^2$ squares the input.a basic square root function $y=\sqrt{x}$ square roots the input. for example, on $y=x^2$ , the coordinate $(2,4)$ is related to the coordinate of $(4,2)$ on $y=\sqrt{x}$ .an input of 2, put into $y=x^2$ , outputs 4. if you use that output as an input into $y=\sqrt{x}$ , you will get the original input of 2.and for coordinates like $(3,9)$ on the parabola corresponds to $(9,3)$ . as for why $y=\sqrt{x}$ is half a parabola: technically, the relation $y = \pm \sqrt{x}$ gives a full sideways parabola (to graph it, graph $y=\sqrt{x}$ and $y=-\sqrt{x}$ at the same time.) but it is not considered a function; a function needs to pass the "vertical line test." square roots of negative numbers are not defined, so the basic $y=\sqrt{x}$ will only give positive answers, thus looking like a bisected parabola.for $y=x^2$ , if you cut the parabola in half so that the domain is $x\geq0$ , then the inverse function (the function that "undoes" the output of $y=x^2$ ) will be the typical $y=\sqrt{x}$ graph. i have attached a picture of this.

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Ответ:

sloane50

22.03.2021

Mathematics

2. Exponential

Step-by-step explanation:

In exponential graphs, each one has the same/similar curvature.

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Why does the graph of a square root function look like half a parabola?

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