Leo asked in Science & MathematicsMathematics · 3 weeks ago

# what is the domain and range of (f)?

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• 3 weeks ago

The DOMAIN of a function is all possible INPUT (x) values.

Start scanning the function going left to right.

The leftmost value is x = -1 (with a solid dot)

The rightmost value is x = 3 (with a solid dot)

And there is a value for every x in between (notice that part of the graph has a solid dot at x=0 and x=2).

So the domain is all values from -1 to 3 inclusive.

Domain = [-1, 3]

The RANGE of a function is all possible OUTPUT (y) values.

So scan the function from bottom to top.

The lowest value is y = -2 (with a solid dot)

The highest value is y = 2 (with a solid dot)

The various parts of the graph cover all values in between.

So the range is all values from -2 to 2 inclusive.

Range = [-2, 2]

P.S. Regarding your answer as a range, you tried to show it as 3 different intervals. If you are going to do that you would need to say it is the *union* of those intervals. Also in interval notation you always show the smaller value in the interval first, then the larger value.

So it seems you were looking to say:

(1, 2] U [-1, 2) U [-2, 1)

But you are listing overlapping intervals and you really just need to say from -2 to 2.

Range = [-2, 2]

• 3 weeks ago

Domain is the possible input, x, values

[-1, 3]

Range is the possible output, y, values

[-2, 2]