SOLUTION: I don't have a scientific calculator, and I need help finding the domain and range for y=3/(x-1)(x+5)
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-> SOLUTION: I don't have a scientific calculator, and I need help finding the domain and range for y=3/(x-1)(x+5)
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Let's start with the domain. What would be the "acceptable" values of x? Really in a rational function, we just don't want to divide by 0. The values that make us 0 is x-1 = 0 and x+5 =0 so x=1 and x=-5. These are the unacceptable values so we'll represent our domain as , .
Now the range. What is the minimum value that y can take on? That's where we have the maximum value in the denominator. Since we're talking about a polynomial in that case, our function approaches infinity (or just some really large number). What happens when we divide by a really large number? We get pretty close to 0.
Now what about the maximum value y can take on? Well, what's the minimum value that our denominator can take on? We can't quite get to 0, but we can get close. If we divide 3 by a very very small number, we'll get a very large number. In fact we'll approach infinity.
So putting that together our range is (0,)
