P.1 Graphs and Models 1
P.1 Graphs and Models
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Which of the following is the correct graph of ?
a. d.
b. e.
c.
2 Chapter P: Preparation for Calculus
____ 2. Which of the following is the correct graph of ?
a. d.
b. e.
c.
P.1 Graphs and Models 3
____ 3. Find all intercepts:
a. x-intercepts: ( ,0), ( ,0); y-intercepts: (0, ), (0, 3)
b. x-intercept: (12, 0); y-intercepts: (0, ), (0, 3)
c. x-intercepts: (4, 0), (–3,0); y-intercept: (0, )
d. x-intercepts: ( , 0), ( ,0); y-intercepts: (0, –12), (0, 12)
e. x-intercept: ( , 0); y-intercept: (0, –12)
____ 4. Find all intercepts:
a. x-intercepts: (–5, 0), (–2, 0), (2, 0); y-intercepts: (0, 0), (0, 10)
b. x-intercepts: (–5, 0), (2, 0); y-intercept: (0, 10)
c. x-intercepts: (–5, 0), (2, 0); y-intercept: (0, –10)
d. x-intercepts: (–5, 0), (–2, 0), (2, 0); y-intercept: (0, 10)
e. x-intercepts: (–5, 0), (–2, 0), (2, 0); y-intercept: (0, –10)
____ 5. Test for symmetry with respect to each axis and to the origin.
a. symmetric with respect to the origin
b. symmetric with respect to the x-axis
c. symmetric with respect to the y-axis
d. no symmetry
e. A, B, and C
____ 6. Test for symmetry with respect to each axis and to the origin.
a. symmetric with respect to the origin
b. symmetric with respect to the y-axis
c. symmetric with respect to the x-axis
d. both B and C
e. no symmetry
4 Chapter P: Preparation for Calculus
____ 7. Sketch the graph of the equation:
a. d.
b. e.
c.
P.1 Graphs and Models 5
____ 8. Sketch the graph of the equation:
a. d.
b. e. none of the above
c.
6 Chapter P: Preparation for Calculus
____ 9. Find the points of intersection of the graphs of the equations:
a.
b.
c.
d.
e.
____ 10. The resistance y in ohms of 1000 feet of solid metal wire at can be
approximated by the model where x is the diameter of the wire in
mils (0.001 in). Use a graphing utility to graph the model
a. d.
P.1 Graphs and Models 7
b. e.
c.
____ 11. The resistance y in ohms of 1000 feet of solid metal wire at can be
approximated by the model where x is the diameter of the wire in
mils (0.001 in). If the diameter of the wire is doubled, the resistance is changed by approximately
what factor? In determining your answer, you can ignore the constant –0.46.
a.
b.
c.
d.
e.
8 Chapter P: Preparation for Calculus
____ 12. Test for symmetry with respect to each axis and to the origin.
a. symmetric with respect to the origin
b. symmetric with respect to the y-axis
c. symmetric with respect to the x-axis
d. both B and C
e. no symmetry
____ 13. Test for symmetry with respect to each axis and to the origin.
a. symmetric with respect to the origin
b. symmetric with respect to the x-axis
c. symmetric with respect to the y-axis
d. no symmetry
e. A, B, and C
____ 14. Find all intercepts:
a. x-intercepts: (0,0), (5,0), (-5,0); y-intercept: (0, -25)
b. x-intercepts: (0,0), (5,0); y-intercept: (0, 0)
c. x-intercepts: (0,0), (5,0), (-5,0); y-intercept: (0, 0)
d. x-intercepts: (0,0), (5,0); y-intercept: (0, 5)
e. x-intercepts: (0,0), (5,0), (25,0); y-intercept: (0, 0)
P.1 Graphs and Models 9
____ 15. Sketch the graph of the equation:
a.
0.511.522.5–0.5–1–1.5–2–2.5 x
0.5
1
1.5
2
2.5
–0.5
–1
–1.5
–2
–2.5
y
d.
12345–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
b.
12345–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
e. none of the above
c.
0.25 0.5 0.75 1 1.25–0.25–0.5–0.75–1–1.25 x
0.25
0.5
0.75
1
1.25
–0.25
–0.5
–0.75
–1
–1.25
y
10 Chapter P: Preparation for Calculus
P.1 Graphs and Models
Answer Section
MULTIPLE CHOICE