MA 121 - Fall 2021 Section G1 - Turn in #2 Eventually Linear Functions

Let f(x) = x2 ? x + 4 and g(x) = x ? 2. x+1

(a) Explain why the graph of f(x) has no horizontal asymptotes.

[5 points]

(b) Using a common denominator, write f(x)?g(x) as a rational function.

[5 points]

(c) If h(x) = f (x) ? g(x) is the rational function in (b), determine lim h(x) as x??

[OVER]

[5 points]

(d) Use the answer in (c) to explain the relationship between the graphs of f(x) and g(x) seen below.

[5 points]

20. 104 y=f (x) y=g (x) -10 0 10 20 30 -10+ -20