Thread: Domain and Range Functions

I am to write this in interval notation. I don't remember learning this:
But here are two examples. On a graph, i know how to get the domain and range, but not from a function.

f(x) = -4 -the radical(9-(x^2))

g(x) = SIN the radical(x^2(-1)

Originally Posted by sgonzalez90

I am to write this in interval notation. I don't remember learning this:
But here are two examples. On a graph, i know how to get the domain and range, but not from a function.

f(x) = -4 -the radical(9-(x^2))

g(x) = SIN the radical(x^2(-1)

Recall that the domain of a function is all possibilities of x at which f(x) is defined:


where is this function defined? Well, you know that you can't take the sqrt of a negative number, s f(x) is defined every where that . (If x where any bigger than 3, 9-x^2 would be less than zero. A big no no unless we're considering complex numbers.)

In interval notation:

you can do the other now can't you?

Originally Posted by VonNemo19

Recall that the domain of a function is all possibilities of x at which f(x) is defined:


where is this function defined? Well, you know that you can't take the sqrt of a negative number, s f(x) is defined every where that . (If x where any bigger than 3, 9-x^2 would be less than zero. A big no no unless we're considering complex numbers.)

In interval notation:

you can do the other now can't you?

great, I understand the concept. But how do we solve for the range?

Solve for x and then determine what y cannot be:













This one requires alittle more thought..........

Ask yourself:

When is the expression under the radical sign negative?

For range I usually look at its graph, or plug values of x into my head.



The domain is [-3, 3]. If you look at only, what is its minimum value? It's 0, when x is -3 or 3. The maximum value? It's 3, when x = 0.

Now consider the whole function. If you plug in x = -3 or 3, you actually get the maximum value of the function, because there is a negative in front of the square root:

Plug in 0 for x to get the minimum value of the function:

The range is [-7, -4].


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