Domain: what numbers can I plug into the equation and still get a valid answer? Since you are taking the square root of x, x has to be 0 or positive. The domain is all real numbers x such that x≥0
Range: What answers will I get if I plug in every valid x in the domain? Normally, taking a square root results in 2 answers, one positive and one negative. However, this is a function and by definition a function can only have one answer (output) for each input value. So, the range is all real numbers≥0
Symmetry: again, normally taking a square root results in 2 answers and that would result in a graph that's symmetrical around the x-axis. However, this is a function and by definition it can't be symmetrical around any horizontal line.
Asymptotes: there are no asymptotes
End notation: the function approaches +∞ as x approaches ∞
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Verified answer
Domain: what numbers can I plug into the equation and still get a valid answer? Since you are taking the square root of x, x has to be 0 or positive. The domain is all real numbers x such that x≥0
Range: What answers will I get if I plug in every valid x in the domain? Normally, taking a square root results in 2 answers, one positive and one negative. However, this is a function and by definition a function can only have one answer (output) for each input value. So, the range is all real numbers≥0
Symmetry: again, normally taking a square root results in 2 answers and that would result in a graph that's symmetrical around the x-axis. However, this is a function and by definition it can't be symmetrical around any horizontal line.
Asymptotes: there are no asymptotes
End notation: the function approaches +∞ as x approaches ∞
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~Sorry if this is wrong... have never done a question like this.
Well, you know x can be any number.
As x gets larger, so too does âx.
As x gets smaller, so too does âx.
Although, as x dips below 0, âx becomes complex.
For example, âx, where x = -4, is +-2i.
Therefore, all x >= 0 will lie on the positive Im. axis, and all x < 0 will result in âxi => (from example) 2i^2 = -2 => negative Re. axis.
It is symmetrical about Im(z) = -Re(z)
Domain: Re(z) < 0
Range: Im(z) >= 0
I don't believe there are any asymptotes, because as x tends to infinity or -infinity, f(x) also tends to infinities.
End notation.. I'm not sure what that is.
N.B. Urgh, sorry, I interpreted the "i" as the constant (root of -1)
Read next answer down.