Activity 3.1.4.
For each of the following prompts, give an example of a function that satisfies the stated characteristics by both providing a formula and sketching a graph.
(a)
A function \(p\) that is always decreasing and decreases at a constant rate.
(b)
A function \(q\) that is always increasing and increases at an increasing rate.
(c)
A function \(r\) that is always increasing for \(t \lt 2\text{,}\) always decreasing for \(t \gt 2\text{,}\) and is always changing at a decreasing rate.
(d)
A function \(s\) that is always increasing and increases at a decreasing rate. (Hint: to find a formula, think about how you might use a transformation of a familiar function.)
(e)
A function \(u\) that is always decreasing and decreases at a decreasing rate.
