# SOLUTION: Make up a rational function that has the following characteristics: crosses the x-axis at 3; touches the x-axis at -2; has a vertical asymptote at x= 1 and at x= -4; has a hole at

Algebra ->  -> SOLUTION: Make up a rational function that has the following characteristics: crosses the x-axis at 3; touches the x-axis at -2; has a vertical asymptote at x= 1 and at x= -4; has a hole at       Log On

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 Click here to see ALL problems on Rational-functions Question 81824: Make up a rational function that has the following characteristics: crosses the x-axis at 3; touches the x-axis at -2; has a vertical asymptote at x= 1 and at x= -4; has a hole at x=5; has a horizontal asymptote at y= 2. Please do try to help me! If you can't figure out the whole thing, then it would be a HUGE help in itself if you could tell me what "touches the x-axis at -2" means. What is the difference between that and crossing the x-axis?Answer by stanbon(60771)   (Show Source): You can put this solution on YOUR website!Make up a rational function that has the following characteristics: crosses the x-axis at 3; Has (x-3) in the numerator. --------------------- touches the x-axis at -2; Has (x+2)^2 in the numerator. -------------------- has a vertical asymptote at x= 1 and at x= -4; Has (x-1) and (x+4) in the denominator --------------- has a hole at x=5; Has (x-5) in the numerator and in the denominator. -------------------- has a horizontal asymptote at y= 2. At this point the degrees of the numerator is 4 and the degree of the denominator is 3 so you need a factor of "2" in the numerator and a factor of "x" in the denominator. ------------------- f(x) = [2(x-3)(x+2)^2(x-5)]/[x(x-1)(x+4)(x-5)] ================== What does "touches the x-axis" mean? Example y=x is a line that "passes thru" the x-axis at x=0. y=x^2 is a parabola that "touches" the x-axis at x=0 This is what "touches" looks like: Cheers, Stan H.