How do you graph $y = \sqrt{x} - 2$ $y=sqrtx-2$ and compare it to the parent graph?

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How do you graph $y = \sqrt{x} - 2$ $y=sqrtx-2$ and compare it to the parent graph?

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Answer 1 · 2018-04-04T02:51:40

$y = \sqrt{x} - 2$ $y=sqrtx-2$ is graphed by shifting the graph of $y = \sqrt{x}$ $y=sqrtx$ down two. $y = \sqrt{x}$ $y=sqrtx$ is basically half of a sideways parabola opening to the right for positive y-values. $y = \sqrt{x}$ $y=sqrtx$ implies $y = + \sqrt{x}$ $y=+sqrtx$ , where y equals the positive square root of x, so inputting a value such as 9 for x yields 3 (as opposed to $y = \pm \sqrt{x}$ $y=+-sqrtx$ which, for 9, yields 3 and -3). Additionally, x cannot be a negative value, so the graph for $y = \sqrt{x}$ $y=sqrtx$ starts at the origin ( $y = \sqrt{0} = 0$ $y=sqrt(0)=0$ ) and curves up and to the right in the first quadrant. $y = \sqrt{x} - 2$ $y=sqrtx-2$ is a transformation of $y = \sqrt{x}$ $y=sqrtx$ two units down (as $y = x - 2$ $y=x-2$ is a transformation of $y = x$ $y=x$ two units down). Thus, the graph of $y = \sqrt{x} - 2$ $y=sqrtx-2$ is:
graph{x^(1/2)-2 [-10, 10, -5, 5]}

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How do you graph $y = \sqrt{x} - 2$ $y=sqrtx-2$ and compare it to the parent graph?

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