domain and range of f(x) = 3x - 2, f(x) = 3x^2 + 4x - 1

[jamieemcclelland]

I am stuck on these problems,

Find the domain and range of each:

f(x) = 3x-2

f(x) = 3x^2 + 4x - 1

There are some others but if anyone knows how to do these kind of problems could somebody please help. Once I know how to do it I will be fine. Thank you!!!

Is the sign for "infinity" a sideways 8? if so then my book has negative infinity as the domain and infinity for the range...can you please explain how they got this answer, it is just not clicking.

 

[tkhunny]

Re: domain and range of functions

Domain
Rule #1 - In the absence of evidence to the contrary, the Domain is ALL Real Numbers
Rule #2 - Look for evidence to the contrary.

Range
This can require a little judgment. What values will the function give? Are there some that cannot be obtained?

 

[tkhunny]

Re: domain and range of functions

"All Real Numbers" is the same as \(\displaystyle (-\infty,\infty)\).

Determining the Domain is a thinking process, not a calculation process. Are there values that don't work? Find them.

Example 1:

\(\displaystyle f(x)\;=\;\frac{1}{x-3}\)

x = 3 doesn't work. Do you see why?

One way to express the answer is \(\displaystyle (-\infty,3)\cup(3,\infty)\).

You can also say, "All Real Numbers except 3".

Example 2:

\(\displaystyle f(x)\;=\;\sqrt{x}\)

x < 0 doesn't work. Do you see why?

One way to express the answer is \(\displaystyle [0,\infty)\).

You can also say, "All NonNegative Real Numbers".

End of Examples:

There are other considerations. You must think about them.