Polynomial Functions

The blue function is the original function f(x) = x³. Which of the following is the correct equation for the red function, g(x)?

• g(x)=x³+1

• g(x)=x³-1

• g(x)=(x-1)³

• g(x)=(x+1)³

Tags

CCSS.HSF.BF.B.3

If the blue is f(x)=x^2, then the red must be

• g(x)=x²-5

• g(x)=x²+5

• g(x)=(x-5)²

• g(x)=(x+5)²

Which equation describes the transformation of shifting f(x)=x³ four units down?

• x³+ 4

• x³- 4

• (x - 4)³

• (x + 4)³

Tags

CCSS.HSF.BF.B.3

Identify the transformations. 

• horizontal shift to the left 2 and vertical stretch by a factor of 3

• horizontal shift to the right 2 and vertical stretch by a factor of 3

• horizontal shift to the right 2 and vertical shrink by a factor of 3

• horizontal shift to the left 2 and vertical shrink by a factor of 3

Tags

CCSS.HSF.BF.B.3

What is the degree of f(x)?

• 3

• 2

• 1

• 0

Describe the end behavior of the function.
y = 4x¹⁰

• down and down

• down and up

• up and down

• up and up

If a zero of a polynomial function has multiplicity 4 that means:

• The x intercept is at (4, 0)

• The graph will "bounce back" at that zero

• The graph will "pass through" at that zero

• Zeros cannot have multiplicity of 4

Polynomial

• an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication.

• An infinite series with increasing powers (exponents) of a variable.

Describe the transformation of y = g(x) for the function

y = 2g(x - 3) + 5

• Shifted right 3 units

  Stretched vertically by a factor of 2

  Shifted up 5 units

• Stretched vertically by a factor of 2

• Shifted left 3 units

  Stretched vertically by a factor of 2

  Shifted down 5 units

• Stretched vertically by a factor of 1/3

Tags

CCSS.HSF.BF.B.3

Which transformation will occur if f(x) = x² is replaced with f(x) + 2?

• Translation left 2 units

• Narrower

• Vertical translation up by 2 units.

• Reflection across the x-axis.