00:01
So in this problem, i'm being asked to write an equation for a rational function that has the following details, the following characteristics.
00:07
Vertical asymptotes at x equals 3 and x equals negative 7, x intercepts at 5 and 1, or 5 .0 ,1, 0 ,0, and a y intercept at 0 .08.
00:18
So first of all, in equation form, each of these vertical asymptotes or x intercepts or solutions came from a factor in this original equation.
00:30
Vertical asymptotes, x equals 3 and x equals negative 7, those are the asymptotes or the x values on my function that make my function undefined, or in other words, that cause my function to divide by 0.
00:43
So the factors in the bottom of this function in the denominator are going to be x minus 3 and x plus 7.
00:51
Because if i set those denominator factors equal to zero, i get x equals three and x equals negative seven being the places on my function, the x values of my function where my function is undefined.
01:04
So those two factors are going to be the denominator.
01:07
In the numerator, when i set my numerator factors equal to zero, that's what gives me my solutions or my x intercepts.
01:14
So my numerator factors are going to be x minus five and x minus one, because setting those, numinator factors equal to zero, get me x equals 5 and x equals 1, which are the solutions or the x intercepts to my function.
01:29
So the last section is the y intercept.
01:32
The y intercept is what happens when instead of setting the function equal to 0 is when i set each of the x values equal to 0.
01:41
So when x equals 0, y needs to equal 8...