Question

3. Determine an equation of a rational function of the form f(x)= ar+b cx+d with x-intercept of 1/4, y-intercept of -1/2, vertical asymptote at x =-2/3, and horizontal asymptote at y = 4/3.

Answer 1

a atb card Ques- Determine an equation of a national function of the form f(x) = The X- inter ceput of /4 , y - inter cept of / vertical asymptote at a at -2/3 and horizontal asympitote at The Given x- unter cepit at ( 10) and vertical asympilote att at 8,0) y = 4/ Ans: ie in } 3 3 le. -2 is the factor of Since vertical asymptorite site at - then denonimator of crational function at -2 is o denominator then denominator of national function is (14%) X - intercept at Ę then Numerator of rational function is 0 at t is factor rool of numerator How ie then numereter of rational function is (x - 2)

Now rational function is (-5 0 at 2 3 * card Now Giuen horizontonal asympitote at y = 4 3 Sinu horizontal asympitate abf a function of type axtb a to make horizontonal asympite te of 0 1 4 3 we multiply 6 by 4 5 because in ♡ { = 1 + 2 irational function 2 42-L 3x+2 New rational functional is = 9.0c f(x) is Nequired Hitional function How we check our rational function is Right now given y intercept at t ie (0,0) Od wrong

Put 2-0 uj we get f(1) = -1/, then our function is Right Prom ② Put a o, we get 1 f(o)= 4X0-1 1.00 +2 = 1 / which is y untercept Hence our function is correct Required Rational function So 42-L 3a+2 Resulti- Rational function of the form aath is 42-L 32+2 cxtd Mote - O if Given function f(x) = axtb card then we find & untercepet by axtb=0 and y intereept put x=0 in ① and veritical card=0 and horizontaal asympitate asympite te Thanking youll