Example: Find the Domain and Range of √(x-3)

1) The Domain is defined as the set of x-values that can be plugged into a function. Here, we can only plug in x-values greater or equal to 3 into the square root function avoiding the content of a square root to be negative.
Thus, domain is x>=3 .
Using Interval Notation we write: [3,∞)

2) The Range of a function is defined as the set of all resulting y values. Here, the lowest y coordinate is y=0 achieved when x=3 is plugged in. The larger the x value plugged in the larger the y coordinate we obtain.
Thus, the range is y>=0 .
Using Interval Notation we write: [0,∞)

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What’s another way to think of Domain and Range?

1) The Domain are the x-values going left (from the smallest x-value) to right (to the largest x-value).

2) The Range are the y-values going from lowest (from the smallest y-value) to highest (to the largest y-value).

What are Domain and Range of a constant Function? In Example y=6 .

1) The Domain is all real numbers. Any number can be plugged into y=6.

2) The Range is just y=6. The lowest and highest y are both 6.