Question

Find the range

Answer 1

@waterineyes
\[f(x) = (x+1)^{2}-1\]

Answer 2

\( y+1=(x+1)^2 \ge 0\) so \( y+1\ge 0\) and \( y\ge -1\)

Answer 3

Can you here do the same process as I did earlier..

Answer 4

yes that was better

Answer 5

f(x) > 3 is the answer

Answer 6

@zaphod in your own words -- what does the word range mean? What does it visually look like?

Answer 7

No @mukushla you have done the same..

Answer 8

zaphod go with mathteacher

Answer 9

f(x) = range
x = domain

Answer 10

@zaphod You've got the right idea, but it's a bit more precise than that.

domain = all VALID input for a function. If you want real numbers as your output (judging by the question, I'm guessing that's the case) there are three things to avoid:

You can't have 1/0
You can't have the square root of a negative number
You can't have the log of 0 or log of anything less than 0.

So when it asks for domain, look for those three things. The domain will be all real numbers EXCEPT where you have 1/0, sqrt( negative) or log (0 ) or log( negative).

The Range = all OUTPUT (y values) of a function. This might be all real numbers or it might be an open or closed subset of real numbers.

sin(x) has range [-1,1]
y = x^2 has range [0, infinity]
etc.

Visually you can see this by graphing the function and looking for asymptotes, or wavy behavior (like with sin). WARNING -- sometimes the graph won't reveal everything! (x^2-1)/(x+1) looks like the line y = x-1 but it is NOT valid at x = -1 because it makes the denominator zero.

I recommend using Geogebra to graph it's free and very easy to use, and makes function transformations a snap :)

Good luck.