+1245 A function f has a horizontal asymptote of y = -4, a vertical asymptote of x = 3, and an x-intercept at (1,0).
Part (a): Let f be of the form \(f(x) = \frac{ax+b}{x+c}\).Find an expression for f(x).
Part (b): Let f be of the form \(f(x) = \frac{rx+s}{2x+t}\).Find an expression for f(x).
Thanks in advance!
+129852 A function f has a horizontal asymptote of y = -4, a vertical asymptote of x = 3, and an x-intercept at (1,0). Find an expression for f(x)....
a) ax + b
______ = f(x)
x + c
If the vertical asymptote is 3, then , in the denominator, 3 + c = 0 and c = -3
If the hrizontla asymptote is -4, then ax / x = -4 ⇒ a = -4
And if the x intercept = ( 1,0), this implies that a(1) + b = 0 ⇒ -4(1) + b = 0 ⇒
-4 + b = 0 ⇒ b = 4
Here is a graph : https://www.desmos.com/calculator/ohx3qy9kvt
+129852 b ) rx + s
_____ = f(x)
2x + t
If the horizontal asymptote = -4, then r / 2 = -4 ⇒ r = -8
If the vertical asymptote = 3, then 2(3) + t = 0 ⇒ 6 + t = 0 ⇒ t = -6
If (1,0) is an x intercept, then r(1) + s = 0 ⇒ -8(1) + s = 0 ⇒ - 8 + s = 0 ⇒
s = 8
Here's a graph : https://www.desmos.com/calculator/cown9bo626
