Question

Given g(t) t-2 t2 - 4 a) Find the horizontal intercepts, if they exist. b) Find the vertical intercept, if it exists. c) Find the vertical asymptotes, if they exist. d) Find the horizontal asymptotes, if they exist. e) Find any holes in the graph, if they exist. f) Sketch a rough graph of y = g(t). Be sure to include all of the information determined above.

Answer 1

t²4 t=2 is a hole so, b ) nuncrator L Degree denominata a) y = 8(1): 1-2 Mote x intercept when y=o t-2 4²_n But note at t=2, there x intercept ie denominator not Y intercept when t. defined 0²h when denominator zero t²n=o (t+2) (t-2)=0 t=2 is holeso, t=-2 is the vertical anyuntate Horizontal asymotote so y=0 is the horizontal asymtote g (o)= 0 - 2 2 = 2 2 2 2 2 y intercept (0,2) vertical asymtotes c) 1-2) = Note 2)

Holes caust on graph of a rational function at input unlre that casuses both numerator and denominator to be zero (+-2) 9 Lt) t²u (t-2) Lt+2) Note t=2 there is a hole t-2 Hote ie g(t)=t-2 t²u t72 (Ex) Lt+2) g(2) = 12 +2) ► Hole =(2, t) glt) vertical Asymbte t=-2 104) tintercept (2, 4) Hole glt) y=0 Horizontal Asymptote