Domain and range?

[bfqt015]

So today was our second day of class, and my Algebra 2 class started the topic of domain and range. Well I'm fine doing input-output tables, but sone of our homework problems are finding the domain and range in equations, which my teacher never taught us. For example, one of the questions is this:

Consider the function y=x^2:
a.) What is it's domain?
b.) What is it's range? (Hint: Think about the kind of number that results when you square either a positive or negative number.)

So, how do I figure this out?! Please help! It's due first period tomorrow morning!

 

[Mrspi]

So today was our second day of class, and my Algebra 2 class started the topic of domain and range. Well I'm fine doing input-output tables, but sone of our homework problems are finding the domain and range in equations, which my teacher never taught us. For example, one of the questions is this:

Consider the function y=x^2:
a.) What is it's domain?
b.) What is it's range? (Hint: Think about the kind of number that results when you square either a positive or negative number.)

So, how do I figure this out?! Please help! It's due first period tomorrow morning!

The "domain" is the set of numbers that are OK to use as "input".

The "range" is the set of numbers that will constitute the "output" of the rule...that is, what are the possible values of y?

Your rule is this:

y = x[sup:3hqsuiut]2[/sup:3hqsuiut]

What numbers are OK to use as values of x? Can you use positive numbers? Can you use 0? Can you use negative numbers? Are fractions and/or decimals all right to use as values for x? The set of all of the numbers which are acceptable values of x is the domain.

Now...the range is the set of possible output values. I suggest you think about what happens when you take an INPUT value, and square it...that's what the rule says you need to do. Can you say anything about what the possible output values must be?


I would suggest that you read the lesson which includes this homework exercise, and study the examples given in that lesson. (There SURELY are some!!)

 

[Deleted member 4993]

So today was our second day of class, and my Algebra 2 class started the topic of domain and range. Well I'm fine doing input-output tables, but sone of our homework problems are finding the domain and range in equations, which my teacher never taught us. For example, one of the questions is this:

Consider the function y=x^2:
a.) What is it's domain?
b.) What is it's range? (Hint: Think about the kind of number that results when you square either a positive or negative number.)

So, how do I figure this out?! Please help! It's due first period tomorrow morning!

What is the definition of the domain of a function?

What is the definition of the range of a function?

Those definitions should help you define those parameters. If you have graphing calculator - graph the given function and look carefully....

 

[bfqt015]

So today was our second day of class, and my Algebra 2 class started the topic of domain and range. Well I'm fine doing input-output tables, but sone of our homework problems are finding the domain and range in equations, which my teacher never taught us. For example, one of the questions is this:

Consider the function y=x^2:
a.) What is it's domain?
b.) What is it's range? (Hint: Think about the kind of number that results when you square either a positive or negative number.)

So, how do I figure this out?! Please help! It's due first period tomorrow morning!

The "domain" is the set of numbers that are OK to use as "input".

The "range" is the set of numbers that will constitute the "output" of the rule...that is, what are the possible values of y?

Your rule is this:

y = x[sup:3btpdddd]2[/sup:3btpdddd]

What numbers are OK to use as values of x? Can you use positive numbers? Can you use 0? Can you use negative numbers? Are fractions and/or decimals all right to use as values for x? The set of all of the numbers which are acceptable values of x is the domain.

Now...the range is the set of possible output values. I suggest you think about what happens when you take an INPUT value, and square it...that's what the rule says you need to do. Can you say anything about what the possible output values must be?


I would suggest that you read the lesson which includes this homework exercise, and study the examples given in that lesson. (There SURELY are some!!)

See, I did, though. That's my problem. I just honestly don't get the whole concept of domain and range. How to figure it out. My book is 8 years old and kind of out-of-depth. And I'm horrid at Algebra. I prefer Geometry, despite proofs an theorems and such. :\

 

[Mrspi]

The terms "domain" and "range" have been around for a very long time, so the fact that your textbook is 8 years old should not make it "out of date."

I've given my best shot at explaining what "domain" and "range" mean...have YOU given your best effort at understanding these concepts?

It's very easy to blame the "bad teacher," the "out of date textbook," "I'm not good at algebra," and so forth...

 

[bfqt015]

I didn't know that the age of the textbook didn't matter... I'm sorry. And I'm not saying he's a bad teacher. In fact, I've heard very good things about him. He just forgot to explain that part. And if what I've been thinking for the past while--that the range equals the function of the domain-- is true, I'm assuming that the answer to letter A is x and that the answer to letter B is 'all counting numbers'. Would that be correct?

 

[mmm4444bot]

the answer to letter A is x and the answer to letter B is 'all counting numbers'. Would that be correct?

No, and no.

The domain of a function is always a set of actual numbers. So is the range.

There is nothing to stop us from squaring any Real number. In other words, we can take ANY number and multiply it by itself. Doing that does not break any rules. (See note in blue at bottom.)

Therefore, every Real number is in the domain of the "squaring" function in your exercise.

There are different ways to write the entire set of Real numbers; I don't know what you've learned, so far.

For the domain, we could write any of the following:

Domain: The set of all Real numbers

Domain: (-?, ?)

Domain: -? < x < ?

Domain: \(\displaystyle \{x | x \in \Re \}\)

Each of these statements says exactly the same thing: every Real number is in the domain.

----------------------------------------------------

The range is also a set of numbers. Specifically, it is the set of this function's outputs. Or, said another way, it is the set of y values that result from squaring every number in the domain.

In other words, if we square every Real number, what set results ? That is the range.

If you're not sure what we get when we square all Real numbers, then start squaring different kinds of Real numbers, and see what happens. Maybe, you'll have an epiphany.

Your teacher also gave you a hint, regarding the range. Do you understand it ?

"Hint: Think about the kind of number that results when you square either a positive or negative number."

-----------------------------------------------------

Here's some more commentary about domains. Not all functions have the entire set of Real numbers as their domain.

EGs:

y = 1/x

The domain of this function cannot include the number zero because division by zero is not defined. In other words, if we tried to use zero as an input to this function, we would be breaking a rule.

Therefore, the domain of this function is "all Real numbers except zero".

y = sqrt(x)

The domain of the "square root" function cannot include any negative numbers because negative numbers do not have square roots, in the Real number system. In other words, if we tried to input a negative number into this function, we would be breaking a rule.

Therefore, the domain of this function is "all non-negative Real numbers".

y = 1/(x + 1)

The domain of this function is "all Real numbers except -1". Do you see why ?

y = sqrt(x + 2)

The domain of this function is "all Real numbers greater than or equal to -2". Do you see why ?

When we're asked to find the domain of a function, we need to think about "illegal" values of x. In other words, values of x that would break a rule, if we tried to input them into the function.