FUNCTION GRAPHS HELP PLEASE

[sungjin6458]

Q) create a rational function that has the following characteristics:
crossses the x axis at 3
touch x axis at -2
Vertical asymptote at x=1
Horiz Asymp at y=2

so far i got: (x-1)(x-3)(x+2)^2 for the demoninator of the function. the numerator is supposed to have (x+3), (x+2)^2, and i think a 2 as the coefficient but i dont get it afterwards

 

[tkhunny]

Q) create a rational function that has the following characteristics:
crossses the x axis at 3
touch x axis at -2
Vertical asymptote at x=1
Horiz Asymp at y=2

so far i got: (x-1)(x-3)(x+2)^2 for the demoninator of the function. the numerator is supposed to have (x+3), (x+2)^2, and i think a 2 as the coefficient but i dont get it afterwards

"crossses the x axis at 3" x-3 good.
"touch x axis at -2" (x-3)*(x+2)^2 good.
"Vertical asymptote at x=1" You wandered off a bit. [(x-3)*(x+2)^2]/(x-1)
"Horiz Asymp at y=2" This one is a little trickier. To get a horizontal asymptote, the degree of the numerator must be less than or equal to the degree of the denominator. No need to make it harder than it is. How about 'x'? It will add a vertical asymptote at x = 0.

2*[(x-3)*(x+2)^2]/[(x-1)*(x^2)]

 

[soroban]

Hello, sungjin6458!

Create a rational function that has the following characteristics:
crossses the x axis at 3
touch x axis at -2
Vertical asymptote at x=1
Horiz Asymp at y=2

I agree with tkhunny . . . your (x - 1) should be in the denominator.

. . . . . . . . (x - 3)(x + 2)²
. . f(x) .= .------------------
. . . . . . . . . . . x - 1

To have a horizontal asymptote y = 2, we need a coefficient of 2
. . and the degrees of the numerator and denominator must be equal.

. . . . . . . . . . 2(x - 3)(x + 2)²
. . . f(x) . = . -------------------
. . . . . . . . . . . . . (x - 1)³