Holt CA Course 1

7-5 Cubic Functions

AF3.1 Graph functions of the form y = nx2 and y = nx3 and use in solving problems.

California Standards

Holt CA Course 1

7-5 Cubic Functions

A cubic function is a function in which the greatest power of the variable is 3. The most basic cubic function is y = nx3 where n ≠ 0.

Holt CA Course 1

7-5 Cubic Functions

Create a table for each cubic function, and use it to graph the function.

Additional Example 1: Graphing Cubic Functions

x x3 y

–2

–1

0

1

2

–2

–0.25

0

0.25

2

A. y = x314

x

y

–2

–2

2

2–4

–4

4

414

(-2)314

(-1)314

(0)314

(1)314

(2)314

Holt CA Course 1

7-5 Cubic Functions

Create a table for each cubic function, and use it to graph the function.

Additional Example 1: Graphing Cubic Functions

x –x3 + 1 y

–2

–1

0

1

2

9

2

1

0

–7

B. y = –x3 + 1

–(–2)3 + 1

–(–1)3 + 1

–(0)3 + 1

–(1)3 + 1

–(2)3 + 1

Holt CA Course 1

7-5 Cubic Functions

Create a table for each cubic function, and use it to graph the function.

Additional Example 1: Graphing Cubic Functions

x x3 – 2 y

–2

–1

0

1

2

–10

–3

–2

–1

6

C. y = x3 – 2

(–2)3 – 2

(–1)3 – 2

(0)3 – 2

(1)3 – 2

(2)3 – 2

Holt CA Course 1

7-5 Cubic Functions

Create a table for each cubic function, and use it to graph the function.

Check It Out! Example 1

A. y = x3 + 114

x x3 + 1 y

–2

–1

0

1

2

–1

0.75

1

1.25

3

x

y

–2

–2

2

2–4

–4

4

414

(-2)3 + 114

(-1)3 + 114

(0)3 + 114

(1)3 + 114

(2)3 + 114

Holt CA Course 1

7-5 Cubic Functions

Create a table for each cubic function, and use it to graph the function.

Check It Out! Example 1

x –x3 – 1 y

–2

–1

0

1

2

7

0

–1

–2

–9

B. y = –x3 – 1

–(–2)3 – 1

–(–1)3 – 1

–(0)3 – 1

–(1)3 – 1

–(2)3 – 1

Holt CA Course 1

7-5 Cubic Functions

Create a table for each cubic function, and use it to graph the function.

Check It Out! Example 1

x x3 + 2 y

–2

–1

0

1

2

–6

1

2

3

10

C. y = x3 + 2

(–2)3 + 2

(–1)3 + 2

(0)3 + 2

(1)3 + 2

(2)3 + 2

Holt CA Course 1

7-5 Cubic Functions

Tell whether the function is linear, quadratic, or cubic.

A.

Additional Example 2: Identifying Types of Functions

The graph is a parabola.Quadratic

Holt CA Course 1

7-5 Cubic Functions

Tell whether the function is linear, quadratic, or cubic.

B.

Additional Example 2: Identifying Types of Functions

The graph curves down, then up.

Cubic

Holt CA Course 1

7-5 Cubic Functions

Tell whether the function is linear, quadratic, or cubic.

C.

Additional Example 2: Identifying Types of Functions

The graph is a parabola.

Quadratic

Holt CA Course 1

7-5 Cubic Functions

Tell whether the function is linear, quadratic, or cubic.

D.

Additional Example 2: Identifying Types of Functions

The graph is a line.

Linear

Holt CA Course 1

7-5 Cubic Functions

Tell whether the function is linear, quadratic, or cubic.

A.

Check It Out! Example 2

The graph is a parabola.

Quadratic

Holt CA Course 1

7-5 Cubic Functions

Tell whether the function is linear, quadratic, or cubic.

B.

Check It Out! Example 2

The graph is a line.

Linear

Holt CA Course 1

7-5 Cubic Functions

Tell whether the function is linear, quadratic, or cubic.

C.

Check It Out! Example 2

The graph curves down, then up.

Cubic

Holt CA Course 1

7-5 Cubic Functions

Tell whether the function is linear, quadratic, or cubic.

D.

Check It Out! Example 2

The graph is a parabola.

Quadratic