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

A. –6k5

B. –6k6

C. 36k5

D. 36k6

Simplify (–6k3)2.

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

A. 2x3y8

B. 2x6y4

C. 4x6y8

D. 16x6y8

Express the area of the square as a monomial.

Over Lesson 9–6

A. 4.08 × 106 km

B. 5.3 × 106 km

C. 9.86 × 108 km

D. 5.3 × 108 km

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.

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. linear

B. nonlinear

C. neither A nor B

D. not a 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.

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. linear

B. nonlinear

C. neither A nor B

D. not a function

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.

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. linear

B. nonlinear

C. neither A nor B

D. not a function

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.

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

Answer: So, this is a nonlinear function.

Solve Subtract to find the changes in price.

Check If you were to graph the function, you would see that the points do not lie on a straight line.

+ 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.

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.

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.