X-hour 1/10 Problems
1. Let f (x) = x2 . Draw the graphs of y = f (x) + 1, y = f (x) − 2, y = f (x + 5), y = f (x − 1),
and y = −f (x).
2. What are the equations of the following graphs obtained from the graph of f (x) = sin(x)?
3. Find values of x, where 0 < x < 0.001, with the following properties:
a. sin(x) = 1
b. sin(x) = 0
c. sin(x) = −1
4. Sketch the graph of an example of a function f that satisfies all of the given conditions:
1. limx→0 f (x) = 1
2. limx→3− f (x) = −2
1
3. limx→3+ f (x) = 2
4. f (0) = −1
5. f (3) = 1.
5. Sketch the graph of the following function and use it to determine the values of a for
which limx→a f (x) exists:


1 + x if x < −1
f (x) = x2 if − 1 ≤ x < 1

2 − x if x ≥ 1
6. Calculate limx→2
x3 −6x2 +3x+10
.
x−2
7. What is
lim
x→0
8. Find lim
x→1
1
1 + 2(1/x)
x2 + 2x − 3
.
x2 + 6x − 7
9. Let


1 + x if x < −1
f (x) = x2 if − 1 ≤ x < 1

2 − x if x ≥ 1
Find limx→−1 f (x) and
limx→1 f (x)
10. Shade in the following regions:
1. |3x + 5| < 1
2. |2y − 1| < 1/2
2