EXERCISE PROBLEMS
1. (14 points) Compute the average rate of change of $f(x) = (x - 1)^2$ over the interval $[1, 1 + h]$
for
(a) $h = 1$
(b) $h = 0.5$
(c) $h = 0.1$
and graphically represent the different average rates of change. What do you observe?
2. (18 points) Describe the following functions in four different ways, that is, (i) in words, (ii)
by a table of values using $x = -2, -1, 0, 1, 2$, (iii) by a graph on the domain $[-3, 3]$, and (iv)
algebraically using the function notation.
(a) The function $f: \mathbb{R} \to \mathbb{R}$ whose value is constant at 3 for all $x$ values in the domain.
(b) The function whose graph is given below:
y
3
3
