For a rational function fx x2x 3x5x 1 a find the vertical...

For a rational function f(x)= (x+2)(x-3)/(x+5)(x-1) A) find the vertical asymptote: x= B) find the x intercept and input as number: x= C) find the horizontal asymptote: y= D) find the y intercept and input as number: y=

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00:01 For this function, this rational, where we have x plus 2, x minus 3 in the numerator, just double checking, as well as x plus 5, x minus 1 in the denominator.

00:18 And to start with the first part, a, with the vertical asymptotes, i like to remind students that it's the non -cancelling factors in the denominator.

00:28 Denominator.

00:32 So non -cancelling and on bottom.

00:35 And you can set each piece equal to zero, although most of my students just haven't memorized that if it's a factor, the vertical asymptote would be the opposite.

00:47 So you subtract five over, same thing with x minus one.

00:50 The reason why you can just do the opposite, you have to do the inverse operation.

00:55 So there's part a, part b, the x intercept, well, the x intercept would be where y equals zero.

01:07 So that's a non -canceling in the numerator.

01:11 Oops, totally misspelled that.

01:18 Now, the reason why i talk about non -cancelling is if they cancel, it's actually not a vertical asymptote or an x intercept, it's actually what we consider it a whole.

01:28 So x plus 2 equal to 0 and x minus 3, but again, it's going to be the opposite because you subtract two over or you add three.

01:38 So that's part b.

01:40 Part c, as for the horizontal asthmpton.

01:43 This is a little bit trickier...

Question

For a rational function f(x)= (x+2)(x-3)/(x+5)(x-1) A) find the vertical asymptote: x= B) find the x intercept and input as number: x= C) find the horizontal asymptote: y= D) find the y intercept and input as number: y=

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