SparklyUnicorn Posted November 23, 2016 Share Posted November 23, 2016 So it says to graph the function: f(x)=(-3x-4)/(x+3) So you figure out the vertical asymptote and the horizontal asymptote. I understand that. Then the y-intercept is figured out by setting x to zero. I get that. The part I'm confused by is figuring the x-intercept. It says the x-intercept is found by setting y equal to 0. (OK, no problem.) But then it says: "Since the rational function is in simplest form, this is equivalent to setting the numerator equal to 0." Ok what? I don't understand this. Might be having a brain fart here, but no why are we only setting the numerator equal to 0 to find the x-intercept? Quote Link to comment Share on other sites More sharing options...
regentrude Posted November 23, 2016 Share Posted November 23, 2016 (edited) Your function can be written as a fraction. In the numerator you have -3x-4. In the denominator you have x+3. A fraction is zero if the numerator is zero (provided that the denominator is not also zero at this position). So, your function is zero if -3x-4 is zero. That gives you -3x=4, x=-4/3. If you put this into the denominator, you see that the denominator is not zero, so there's your x intercept. Edited November 23, 2016 by regentrude 4 Quote Link to comment Share on other sites More sharing options...
maize Posted November 23, 2016 Share Posted November 23, 2016 When the numerator is zero y can only be zero. I'm not quite sure what you are asking. 1 Quote Link to comment Share on other sites More sharing options...
kiana Posted November 23, 2016 Share Posted November 23, 2016 When a fraction is zero, this means that the numerator must be zero and the denominator must not be (because 0/0 is undefined). Or more algebraically, if a/b = 0, a = 0 and b != 0. 1 Quote Link to comment Share on other sites More sharing options...
EKS Posted November 23, 2016 Share Posted November 23, 2016 You could also set the whole thing equal to zero, but setting the numerator equal to zero is a (very small) shortcut. Here's why: 0 = (-3x-4)/(x+3) Multiply both sides by (x+3) 0 = (-3x-4) Now the numerator is set equal to zero Be sure to check the solution to make sure that it doesn't make the denominator zero (it's not an issue with this problem). The other way to think of it is that if the numerator of a fraction is zero, then the whole thing is zero. 1 Quote Link to comment Share on other sites More sharing options...
SparklyUnicorn Posted November 23, 2016 Author Share Posted November 23, 2016 Thank you! Quote Link to comment Share on other sites More sharing options...
SparklyUnicorn Posted November 23, 2016 Author Share Posted November 23, 2016 You could also set the whole thing equal to zero, but setting the numerator equal to zero is a (very small) shortcut. Here's why: 0 = (-3x-4)/(x+3) Multiply both sides by (x+3) 0 = (-3x-4) Now the numerator is set equal to zero Be sure to check the solution to make sure that it doesn't make the denominator zero (it's not an issue with this problem). The other way to think of it is that if the numerator of a fraction is zero, then the whole thing is zero. Ah! See I did do this, but for some dumb reason instead of multiplying by zero, I multiplied by 1. I got the right answer a couple of times because it just so happened to work out that way. I find it most helpful to do it this way. Quote Link to comment Share on other sites More sharing options...
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