Write a rational function f that has vertical asymptote at x=2, a horizontal asymptote at y=3 and a zero at x=−1.
y=f(x)g(x)
Vertical asymptode at r=2
y⟶∞,x=2
y=f(x)x−2
Zero at x=−1
y=a(x+1)x−2
xy−2y=a+2y
x=a+2yy−a
y→3,x→∞
a=3
y=3(x+1)x−2
Let f(x)=⎧⎨⎩∣∣x2−3x∣∣+a,0≤x<32−2x+3 x≥32 If f(x) has a local maximum at x =.
f(x)={3x+5if x≥2x2,if x<2 Discuss the continuity of f(x) at x=2.