domain and range of y = 4 - x^2, y = 2 + sqrt(x - 1), y = -

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dummiesx3

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Sep 10, 2008
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hi, i just got this for hw,and i dont know how to do this problem! plz help.....what do i do first?

Find the domain and range of :

1) y=4-x^2

2) y= 2+ sqrt(x-1)

3)y= -sqrt(-x)

anything will help, plz tell me what i should do to solve these problems....how do i find the domain and range.......its so confusing.....im so lost... :!:
 
Re: review

dummiesx3 said:
Find the domain and range of :

1) y=4-x^2

2) y= 2+ sqrt(x-1)

3)y= -sqrt(-x)

... its so confusing ... im so lost ...
Click to expand...

Hello X3:

If you are confused, then you probably don't understand the definitions of the terms domain and range.

(You did not post anything other than your assignment. So, I have to GUESS at what kind of help you need.)

Have you learned about functions? I'm not sure which terminology to use for you because you did not provide us with any information about what you already know, so I have to GUESS.

When thinking about the domain of a function, you need to be aware of things like division by zero and taking the square root of a negative value. You may not input any value for X that causes things like this to happen.

You can think of a function as a machine which spits out a corresponding Y value for any value of X that you shove into it.

Here's a simple model:

\(\displaystyle \mbox{X} \;\longrightarrow\; \boxed{f} \;\longrightarrow\; \mbox{Y}\)

This model shows a function named f. You shove a value of X into one end, and the corresponding value of Y comes out the other.

Some values of X are illegal! Functions cannot accept ANY illegal values! You need to be aware of some restrictions in mathematics; two of the main restrictions are 1) you can't divide by zero; and 2) you can't take the square root (or any even root) of a negative value.

HERE ARE THE DEFINITIONS for domain and range.

The domain of a function is A SET OF NUMBERS.

It is the set of all legal values that the function will accept. In other words, the domain is the set of all valid Xs.

The range of a function is A SET OF NUMBERS.

It is the set of all values that come out of the function after inputting every number from the domain. In other words, the range is the set of all corresponding Ys.

Here's the model for the function in your second exercise.

\(\displaystyle \mbox{X} \;\longrightarrow\; \boxed{2 + \sqrt{x - 1}} \;\longrightarrow\; \mbox{Y}\)

This function is DEFINED by the expression 2 + sqrt(x - 1).

We do not need to be concerned about division by zero because there is no division taking place in the expression above that defines the function.

But, we do need to be aware that the value of X - 1 can never be negative.

In other words, we need the value of the expression X - 1 to be greater than (or equal to) zero, in order to be sure that we're not trying to take the square root of a negative value.

Can you figure out the set of numbers for X that will not cause the expression X - 1 to be negative? If you can find this set of numbers, then you have found the DOMAIN of the function.

After you determine the domain, then think about the set of Y values that come out of this function when you input all of the X values from the domain. If you can find this set of Y values, then you have found the RANGE of the function.

In summary, the domain of a function is ALL REAL NUMBERS, unless you find some numbers that are illegal; in this case, you must eliminate them. The range of a function is all numbers that result from using the domain.

In addition to the model of a function, there are other ways to "visualize" the domain and range. You can look at a graph of a function, for example, and see the domain as a "shadow" cast onto the X-axis by the function's graph. You can see the range at a "shadow" cast onto the Y-axis by the function's graph.

If you need more help with these concepts, then please post your work and let us know why you're stuck.

Cheers,

~ Mark :)
 
Re: domain and range

ok thanx, i get it

here are my answers

y=4-x^2

Domain: all real #s
Range: y<=4


y=x^2 -9

Doomain: all real #s
Range: y>= -9


y=2+ sqrt(x-1)

domain: x>=1
range: y>=2


y=-sqrt(-x)

domain: x>=0
range:y<=0


are they correct? did i do it right?
 
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