Which function has a domain of and a range of

Asked by wiki @ 10/06/2021 in Mathematics viewed by 270 People

Which function has the domain of x≥5 and a range of y≤3?

Answered by wiki @ 10/06/2021

The domain of the function are all possible values for variable x and the range of the function are all possible values for the variable y.

Consider the parrent function $y=\sqrt{x}.$ The domain of this function is $x\ge 0,$ the range of this function is $y\ge 0.$

1. Translate this function 5 units to the right. After this translation the function becomes

$y=\sqrt{x-5}.$

2. Reflect previous function about the x-axis, then the expresssion of the new function is

$y=-\sqrt{x-5}.$

The range of the function will be $y\le 0.$

3. Translate the function $y=-\sqrt{x-5}$ 3 units up, then you will get the function

$y=-\sqrt{x-5}+3.$

The domain of this function is $x\ge 5,$ the range of this function is $y\le 3.$

Answer: $y=-\sqrt{x-5}+3.$

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