Anonymous
Anonymous asked in Science & MathematicsMathematics · 7 years ago

# What would be the Domain and Range of this. s(x) = 2 / (x + 2)?

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• 7 years ago

Domain = all the values of x for which the function (s) will give you a "well-defined" answer.

well-defined = for a given value of x, the function will spit out one, and only one, clear answer.

In real numbers, we normally begin by assiming that the domain contains ALL real numbers, then we remove any number that causes a problem. Here, you have a division, so we would check for values of x that would cause a division by zero (they are NOT well-defined).

The value x = -2 gets removed from the rest of the numbers, and what is left is the domain.

(-infinity, -2)U(-2, +infinity)

Range is the set of possible values that s can take, once you have tried all values in the domain.

Here, you should check the "end behaviour" (what happens as the value of x goes very high in the positive, and very high in the negative). At first glance, I would say that it is impossible to get s(x) = 0, but you better check that.

You can get extremely close to 0, but not exactly at zero.

Any other number seems possible.

• 7 years ago

Domain: x ≠ -2

Range: all real numbers except 0