Modelling Polynomial Functions

Classify the polynomial by degree.

• quartic

• quintic

• 6th degree polynomial 

• 7th degree polynomial

How many relative extrema(tuning points) are in the picture?

• 2

• 3

• 4

• 5

The function shown has:

• Degree two with negative leading coefficient.

• Degree three with negative leading coefficient.

• Degree four with negative leading coefficient.

• Degree four with positive leading coefficient.

Which of the following could be a possible equation for the function shown?

• f(x) =-2x³ + x² - 5x + 1

• f(x) = 2x³ - 4x² + x + 1

• f(x) = 3x² + 5x + 1

• f(x) = -2x³ +3x - 1

Which of the following functions contain line symmetry?

• g(x) = 3x³ + 2x²

• g(x) = 5x⁴ + 3x³ + 4x²

• g(x) = 3x⁶

• g(x) = 18x³

Which of the following functions could represent the graph shown?

• f(x) = -2x⁵

• f(x) = -2x⁴ + 7x³ + 3x² -5x + 8

• f(x) = 2x⁵ + 3x⁴ - 3x³ + 5x² - 3x + 4

• None of these functions could represent the graph shown.

Which description best matches the function shown:

• Odd degree with positive leading coefficient.

• Even degree with positive leading coefficient.

• Degree three, with negative leading coefficient.

• Degree four, with negative leading coefficient.

The function f(x) = -5x⁴ + 3x² - 3x + 5

• Extends from quadrant 2 to quadrant 1.

• Extends from quadrant 2 to quadrant 4.

• Extends from quadrant 3 to quadrant 1.

• Extends from quadrant 3 to quadrant 4.

The function shown contains:

• Only one local maximum.

• Two local maximums.

• Two local minimums.

• Three local maximums

What is the equation in factored form of this graph?

• f(x) = (x-4)(x-1)²(x+2)(x+4)

• f(x) = (x-4)(x+1)²(x+2)(x+4)

• f(x) = (x-4)(x-1)²(x-2)(x+4)

• f(x) = (x+4)(x+1)²(x-2)(x-4)