How do you graph $y = \sqrt{x} - 3$ $y=sqrtx-3$ , compare it to the parent graph and what is the domain and range?

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How do you graph $y = \sqrt{x} - 3$ $y=sqrtx-3$ , compare it to the parent graph and what is the domain and range?

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Answer 1 · 2017-08-27T11:24:31

Standard graph of $y = \sqrt{x}$ $y=sqrtx$ transformed (shifted) 3 units negative (down) on the $y -$ $y-$ axis.
Domain; [0, +oo); Range: [-3, +oo)

Explanation:

$y = \sqrt{x} - 3$ $y = sqrtx-3$

Graphically, $y$ $y$ is the standard graph of $y = \sqrt{x}$ $y = sqrtx$ transformed (shifted) 3 units negative (down) on the $y -$ $y-$ axis. As can be seen by the graph of $y$ $y$ beow.

graph{sqrtx-3 [-1.28, 16.5, -4.204, 4.686]}

$y in RR$ is defined where $x>=0$

Hence, the domain of $y$ is $[0, +oo)$

Then, $y_min = y(0) = -3$

Since $y$ has no upper bound, the range of $y$ is [-3, +oo)

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How do you graph $y = \sqrt{x} - 3$ $y=sqrtx-3$ , compare it to the parent graph and what is the domain and range?

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How do you graph y=sqrtx-3y=√x−3y=sqrtx-3, compare it to the parent graph and what is the domain and range?

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How do you graph $y = \sqrt{x} - 3$ $y=sqrtx-3$ , compare it to the parent graph and what is the domain and range?