Question

What is the domain and range for y=sqrt(x-4)

Answer 1

domain is found by solving x-4>=0
the range is found by thinking of the outputs
the outputs can range from 0 to infinity

Answer 2

Domain: set of all numbers that can be inputted into a function

Since you cannot take the square root of a negative number, this means that x-4 CANNOT be negative. So it's either 0 or it's positive.


So..

\[x-4\ge0\]

\[x-4+4\ge0+4\]

\[x\ge4\]


So this says: "Any number greater than or equal to 4 will result in x-4 being either 0 or some positive number"


So this means that the domain is \[\large \left\{x|x\ge4\right\}\]

This basically says: "the domain is the set of all numbers x such that x is greater than or equal to 4"


In interval notation, the domain is \[ [4,\infty)\]

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The range is the set of all possible outputs. We can find the most extreme point of the range by plugging in the most extreme value for the domain


\[\sqrt{x-4}=\sqrt{4-4}=\sqrt{0}=0\]


So the smallest possible output is y=0, which means that the range is \[\large \left\{y|y\ge0\right\}\]

This basically says: "the range is the set of all numbers y such that y is greater than or equal to 0"


In interval notation, the range is \[ [0,\infty)\]

Answer 3

lol wow jim

Answer 4

lol yes there's a lot to domain and range