How do you graph $y = \sqrt{x} - 2$ $y=sqrtx-2$ and what is the domain and range?

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How do you graph $y = \sqrt{x} - 2$ $y=sqrtx-2$ and what is the domain and range?

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Answer 1 · 2018-02-21T12:47:37

See below.

Explanation:

The graph looks like this:

graph{sqrt(x)-2 [-10, 10, -5, 5]}

The domain is all possible values of $x$ $x$ that give out a defined value of $f (x)$ $f(x)$ .

Here, $y$ $y$ will be undefined if $x < 0$ $x<0$ , as the square root function cannot, really, have an input below $0$ $0$

So $x \geq 0$ $x>=0$ .

In interval notation, the domain is $[0, \infty)$ $[0,oo)$ .

The range is all possible outputs of $f (x)$ $f(x)$ .

Since a square root function does not give an answer above $0$ $0$ , the range of $\sqrt{x}$ $sqrt(x)$ is $y \geq 0$ $y>=0$ . However, since the above function is $\sqrt{x} - 2$ $sqrt(x)-2$ , the range is $y \geq - 2$ $y>=-2$ , or in interval notation:

$[- 2, \infty)$ $[-2,oo)$ .

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How do you graph $y = \sqrt{x} - 2$ $y=sqrtx-2$ and what is the domain and range?

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Explanation:

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