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Calculus I, Fall 2023
Assignment 1
Question 1. (4 Points)
(a) What is your major?
(b) Have you taken Calculus before, and if so, when and where?
Question 2. (10 Points) Create a Function
6 y
4
2
−6
−4
2
−2
4
x
6
−2
−4
−6
On the figure above, sketch the graph of a function y = f (x) that satisfies the following conditions:
• f (0) = 2,
• for every x > 0, f (x) = −2, and
• f (−3) = −4,
• f (x) is increasing on the interval [−6, 0).
• f is defined everywhere,
2
Question 3. (10 Points) Let f be the function so that, for every real number x,
f (x) =
7 if x ≥ 2
.
1


if x < 2
x−2



(a) Evaluate f (−3).
(c) Evaluate f (2).
(b) Evaluate f (−3/10), and simplify your answer. (d) Let t be a real number, so that t < 2. Evaluate f (t).
(Don’t overthink this.)
(e) What is the domain of f ?
3
Question 4. (6 Points)
Consider the graph of the function y = f (x) given below.
y
6
4
Pattern Continues →
2
x
3
−2
For the following, find each of the quantities. If a quantity does not exist, write "DNE" and then explain
why.
(a) lim f (x) =
x→−2
(d) lim− f (x) =
(b) lim f (x) =
x→0
(e) lim+ f (x) =
(c) f (3) =
(f) lim f (x) =
x→3
x→3
x→3
4