Domain and Range????

Question

I have an algebra question about domain and range of a function...1st of all, what the heck does that mean??? Here's the function =)
y= |x+4|

yeah, how the flippin heck do i do that???????

Answer 1

y = |x+4|
The bars mean it is the absolute value of (x+4)
You can take the absolute value of any number. Since x+4 has no restrictions that means the domain is all real numbers.
When ou take the absolute value of a number, it turns a number positive. For instance |-3| = 3
If a number is not negative, then it just stays the same.
|7| = 7
|0| = 0
Therefore, the range is all real numbers greater than or equal to zero.

Answer 2

domain means what x values could legitimately be put into the function. Here as the others have said, there is no restriction, since we are simply doing the absolute value of the sum of x and 4. The range of a function is all the possible values that could result. And as the others have said, since absolute value changes the sign to positive, the only results are 0 and all positive numbers, so its range is that.

There are other functions that would not work this way. For instance, y = 1/x. Since 1/0 is undefined, 0 could not be included in the domain, so its domain is the set of all real numbers except 0. For the range, there is (coincidentally) no way to get 0 as a result, so it would also be left out of the range. So its range is also all real numbers except 0.

Another example is y = sin x. Here the domain can be anything. The sin function, however, only produces results of -1 to 1, so that is its range.

Answer 3

The domain of a function, in simple terms, is "what values can x be?" and the range of a function is "what values can y be?"

y = |x+4| uses the "absolute value" function (which is what the vertical bars mean). Absolute value is defined as follows:

|x| = { x if x >= 0, and -x if x < 0.

That is, any positive number stays the same when taking the absolute value, and any negative number becomes a positive number.

In the above case of finding the domain of y = |x+4|, asking the question "What values can x be?" x can be any real number because the absolute value function doesn't care whether what's inside is positive or negative. The range, however, i.e. "what values can y be", is different. The result of any absolute value is a positive number greater than or equal to zero.

Therefore, Domain: All real numbers, or (-infinity,infinity)
Range: [0,infinity)

Answer 4

domain= all real numbers
range: since the function is an absolute value function, that means that all the possible values of y >=0 ............!

Answer 5

from all x values to values of y>=0

Answer 6

domain is all real numbers
and range is all positive numbers