For each of the following scenarios give an example function f (x) which satisfies the conditions provided, and sketch f (x)

around this limiting behaviour.

a. lim x→−∞

f (x) → ∞, where f (x) is not linear.

b. lim x→∞

f (x) = 3, where f (x) is not constant.

c. lim x→5 f (x) → −∞.

d. lim x→5 f (x) = 3, where f (5) does not exist.