Can someone explain how to solve for the invariant for 6b or c?
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It's not clear what you want to do. You say "find the invariant" but there is no mention of "invariant" in the problem. The problem asks you to find the "domain, intercepts, asymptotes, and positive/negative intervals". Okay, what have you done so far? Do you know how to find the domain for a rational (fraction) function? Do you know what intercepts and asymptotes are?