Question

The distance of an object falling is a function of time t and can be expressed as s(t) = −16t². Graph the function and determine if it is one-to-one.

Answer 1

Given s(t) = –16t²

s(t₁) = s(t₂)

⇒ –16t₁² = –16t₂²

⇒ t₁² = t₂²

⇒ ± t₁ = ± t₂

Since s(t₁) = s(t₁) 

⇒ 14t₁ = t₂

∴ The function s(t) is not one-one

Graph of s(t) = –16t²

Take the time along x-axis and distance along y-axis.

t	0	1	2	3
s(t)	0	– 16	– 64	– 144