Five-Minute Check (over Lesson 9–6)
Then/Now
New Vocabulary
Example 1: Identify Functions Using Graphs
Example 2: Identify Functions Using Equations
Example 3: Identify Functions Using Tables
Example 4: Real-World Example: Real-Life
Functions
Over Lesson 9–6
Simplify 5(x2)–5.
A. 5x10
B. –5x10
C.
D.
Over Lesson 9–6
Simplify (–6k3)2.
A. –6k5
B. –6k6
C. 36k5
D. 36k6
Over Lesson 9–6
Simplify (3s6v4)–3.
A.
B.
C.
D.
Over Lesson 9–6
Simplify (–b–1)3.
A.
B.
C. –b3
D. b3
Over Lesson 9–6
Express the area of the square
as a monomial.
A. 2x3y8
B. 2x6y4
C. 4x6y8
D. 16x6y8
Over Lesson 9–6
The radius of the Earth at the equator is about
1.3 × 104 kilometers long. Use the formula
A = 3.14 × r 2 to find the approximate area of a cross
section of the Earth at the equator.
A. 4.08 × 106 km
B. 5.3 × 106 km
C. 9.86 × 108 km
D. 5.3 × 108 km
You have already represented linear functions
using graphs, equations, and tables.
(Lesson 8–3)
• Determine whether a function is linear or
nonlinear from a graph.
• Determine whether a function is linear or
nonlinear from an equation or table.
• nonlinear function
Identify Functions Using Graphs
A. Determine whether the
graph represents a linear
or nonlinear function.
Answer: The graph is a straight line, so it
represents a linear function.
Identify Functions Using Graphs
B. Determine whether the
graph represents a linear or
nonlinear function.
Answer: The graph is a curve, not a straight line,
so it represents a nonlinear function.
A. Determine whether the graph represents a linear
or nonlinear function.
A. linear
B. nonlinear
C. neither A nor B
D. not a function
B. Determine whether the graph represents a linear
or nonlinear function.
A. linear
B. nonlinear
C. neither A nor B
D. not a function
Identify Functions Using Equations
A. Determine whether y = –5x – 4 represents a
linear or nonlinear function.
Answer: This equation represents a linear function
because it is written in the form y = mx + b.
Identify Functions Using Equations
B. Determine whether y = 2x2 + 3 represents a linear
or nonlinear function.
Answer: This equation is nonlinear because x is raised
to the second power and the equation cannot
be written in the form y = mx + b.
A. Determine whether the equation y = x2 + 2x – 1
represents a linear or nonlinear function.
A. linear
B. nonlinear
C. neither A nor B
D. not a function
B. Determine whether the equation
represents a linear or nonlinear function.
A. linear
B. nonlinear
C. neither A nor B
D. not a function
Identify Functions Using Tables
A. Determine whether the table represents a linear
or nonlinear function.
As x increases by 2,
y decreases by 8.
So, this is a linear function.
Answer: linear
Identify Functions Using Equations
B. Determine whether the table represents a linear
or nonlinear function.
As x increases by 3,
y increases by a greater
amount each time. So,
this is a nonlinear
function.
Answer: nonlinear
A. Determine whether the table represents a linear or
nonlinear function.
A. linear
B. nonlinear
C. neither A nor B
D. not a function
B. Determine whether the table represents a linear or
nonlinear function.
A. linear
B. nonlinear
C. neither A nor B
D. not a function
Real-Life Functions
OIL The table shows the price of oil
futures per barrel for six months.
Describe whether the data
represents a linear or nonlinear
function.
Understand You need to determine whether the data
represents a linear or nonlinear
function.
Plan
Find the change in price for each month.
Make a table.
Real-Life Functions
Solve
Subtract to find the changes in price.
+ 0.13
– 0.13
– 0.18
– 0.26
– 0.50
As the months increase by 1, the price changes by a
different amount each time.
Answer: So, this is a nonlinear function.
Check If you were to graph the function, you would
see that the points do not lie on a straight line.
OIL The table shows the price
of oil futures per barrel of oil for
six months. Describe whether
the data represent a linear or
nonlinear function.
A.
Linear; the price changes by the same
amount each month.
B.
Linear, the price changes by different
amount each month.
C.
Nonlinear; the price changes by the
same amount each month.
D.
Nonlinear, the price changes by
different amounts each month.