Cubic Graph Transformations and Characteristics

Name the parent function.

• cubic
• cube root
• exponential
• quadratic

Describe the transformation of the graph y = (x)³ + 6

• Horizontal shift right 6

• Horizontal shift left 6

• Vertical shift up 6

• Vertical shift down 6

What transformations has the function undergone?

• reflect over the y-axis, vertical compression by a factor of 2, vertical down right 5, horizontal shift right 1

• reflect over the x-axis, horizontal compression by a factor of 2, left 5, up 1

• reflect over the x-axis, vertical stretch by 2, horizontal shift right 5, vertical shift up 1

• reflect over the y-axis, horizontal stretch by a factor of -2, horizontal shift right 5, and vertical shift up 1

What are the transformations?

y=(x-2)³+4

• Horizontal shift right 2. Vertical shift up 4

• Horizontal shift left 2. Vertical shift down 4

• Horizontal shift right 2. Vertical shift down 4

• Horizontal shift left 2. Vertical shift up 4

Describe the transformation of the graph  y = -2(x + 5)³ 

• Shrink by 2, Reflected over y-axis, Right 5
• Stretch by 2, Reflected over x-axis, Left 5
• Stretch by 2, Reflected over x-axis, Right 5
• Shrink by 2, reflected over y-axis, Left 5

Describe the transformation of the graph  y = - ½(x + 4)³ - 1

• Left 4 and Down 1
• Reflected x-axis, Down 1, Left 4, Shrink by 1/2
• Reflected x-axis, Down 1, Left 4, Stretch by 1/2
• Reflected x-axis, Up 1, Right 4, Shrink by 1/2

Describe the transformation of the graph  
y = ½x³

• Vertical compression by 1/2
• Horizontal compression by 1/2
• Vertical stretch by 2
• Horizontal stretch by 2

Describe the transformation of the graph  
y = (2x)³

• Vertical compression by 1/2
• Horizontal compression by 1/2
• Vertical stretch by 2
• Horizontal stretch by 2

Describe the transformation of the graph  
y =  (½x)³

• Vertical compression by 1/2
• Horizontal compression by 1/2
• Vertical stretch by 2
• Horizontal stretch by 2

Describe the transformation of the graph  
y = 2x³

• Vertical compression by 1/2
• Horizontal compression by 1/2
• Vertical stretch by 2
• Horizontal stretch by 2