None of those require a calculator. Domain and range can be found by observing the function and it's inverse and finding out the points where it isn't defined. Exclude those points and you get the domain and range. Asymptotes are basically those points you excluded while finding the domain and range. x intercept is the point where y = 0 and y intercept is the point where x = 0. For any given question, all these barely takes 2-3 minutes with good practice. More on reddit.com

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The TI-89 does not have a built-in function for range and domain, but there are plenty of programs for it that will calculate it. I found one here . More on reddit.com

technically the domain is part of the definition of a function and you can have different domains with the same functional equation for example we can have: f: R- to R with f(x)=1/x and g: R+ to R with g(x)=1/x so if I tell you h(x)=1/x you have no information about the domain however in applied math people usually just use a functional equation to represent a function and implicitely set the domain as the biggest possible subset within the real numbers so in the case of our example the function h can accept any real number except 0, hence its biggest possible domain is R \ {0} such that: h: R \ {0} to R with h(x)=1/x so the general strategy is to look for problematic values that cause division by zero or similar issues (like square root from negative numbers) and to exclude them consider for example: f(x)=sqrt(1-x2 ) in this case the problematic values are all x such that: 1-x2 <0 iff 1 < x2 iff 1 < |x| so the domain of f is all real numbers except those with an absolute values bigger than 1, which means only values between -1 and 1 are allowed: f: [-1, 1] to R, f(x)=sqrt(1-x2 ) More on reddit.com