Five-Minute Check (over Lesson 1–5)
CCSS
Then/Now
New Vocabulary
Example 1: Representations of a Relation
Example 2: Real-World Example: Independent and
Dependent Variables
Example 3: Analyze Graphs
Over Lesson 1–5
What is the solution of 5b – 11 = 34 given the
replacement set {7, 9, 13, 16, 22}?
A. 7
B. 9
C. 13
D. 16
Over Lesson 1–5
A.
B.
C.
D.
Over Lesson 1–5
Solve (6 – 42 ÷ 7) + k = 4.
A. 6
B. 4
C. 0
D. –1
Over Lesson 1–5
Solve (3 + 42 – 9)m = 90.
A. 15
B. 10
C. 9
D. 5
Over Lesson 1–5
Solve 8a – (15 – 3.2) = a + (52 – 13).
A. 3.8
B. 3.6
C. 3.4
D. 3.0
Over Lesson 1–5
A. 896
B. 104
C. 42
D. 24
Content Standards
A.REI.10 Understand that the graph of an equation in two
variables is the set of all its solutions plotted in the
coordinate plane, often forming a curve (which could be a
line).
F.IF.1 Understand that a function from one set (called the
domain) to another set (called the range) assigns to each
element of the domain exactly one element of the range. If
f is a function and x is an element of its domain, then f(x)
denotes the output of f corresponding to the input x. The
graph of f is the graph of the equation y = f(x).
Mathematical Practices
1 Make sense of problems and persevere in solving them.
Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State
School Officers. All rights reserved.
You solved equations with one or two
variables.
• Represent relations.
• Interpret graphs of relations.
• coordinate system
• relation
• coordinate plane
• mapping
• x- and y-axes
• domain
• origin
• range
• ordered pair
• independent variable
• x- and y-coordinates
• dependent variable
Representations of a Relation
A. Express the relation {(4, 3), (–2, –1), (2, –4), (0, –4)}
as a table, a graph, and a mapping.
Table List the x-coordinates
in the first column and the
corresponding y-coordinates
in the second column.
Representations of a Relation
Graph Graph each ordered pair on a coordinate plane.
Representations of a Relation
Mapping List the x-values in the domain and the
y-values in the range. Draw an arrow from the x-value
to the corresponding y-value.
Domain
4
–2
2
0
Range
3
–1
–4
Representations of a Relation
B. Determine the domain and range for the
relation {(4, 3), (–2, –1), (2, –4), (0, –4)}.
Answer: The domain for this relation is {4, –2, 2, 0}. The
range is {3, –1, –4}.
A. Express the relation {(3, –2), (4, 6), (5, 2), (–1, 3)}
as a mapping.
A.
C.
B.
D.
B. Determine the domain and range of the relation
{(3, –2), (4, 6), (5, 2), (–1, 3)}.
A. D = {–1, 3, 4, 5}; R = {–2, 2, 3, 6}
B. D = {–2, 2, 3, 6}; R = {–1, 3, 4, 5}
C. D = {–1, 3}; R = {–2, 2}
D. D = {4}; R = {4}
Independent and Dependent Variables
A. CLIMATE In warm climates, the average amount
of electricity used rises as the daily average
temperature increases, and falls as the daily
average temperature decreases. Identify the
independent and the dependent variables for this
function.
Answer: Temperature is the independent variable, as it
is unaffected by the amount of electricity used.
Electricity usage is the dependent variable, as
it is affected by the temperature.
Independent and Dependent Variables
B. The number of calories you burn increases as
the number of minutes that you walk increases.
Identify the independent and the dependent
variables for this function.
Answer: The time is the independent variable. The
number of calories burned is the dependent
variable, as it is affected by the time.
A. In a particular club, as membership dues increase,
the number of new members decreases. Identify the
independent and dependent variable in this function.
A. The number of new members is
the independent variable. The
dues is the dependent variable.
B. Membership dues is the
independent variable. The
number of new members is the
dependent variable.
C. x is the independent variable.
y is the dependent variable.
D. Both variables are independent.
B. The area of a square increases as the length of a
side increases. Identify the independent and
dependent variable in this function.
A. The length of the side is
independent, and the the area of
the square is dependent.
B. The area is independent, and the
side length is dependent.
C. Both variables are independent.
D. Both variables are dependent.
Analyze Graphs
The graph represents the temperature in Ms. Ling’s
classroom on a winter school day. Describe what is
happening in the graph.
Sample answer: The temperature increases after the
heat is turned on. Then the
temperature fluctuates up and down
because of the thermostat. Finally, the
temperature drops when the heat is
turned off.
The graph represents Macy’s
speed as she swims laps in a pool.
Describe what is happening in the
graph.
A. Macy is doing bobs.
B. Macy’s speed increases as she
crosses the length of the pool, but
then decreases to zero when she
turns around at the end of each lap.
C. Macy is swimming at a constant
speed.
D. Macy’s speed continues to decrease.