Multiplicity of Polynomials and Graphs

Which function has a root with a multiplicity greater than 1?

• A

• B

• C

• D

Based on the x-intercepts, shape, and end behavior shown, which of the following could be an equation for the function shown?

• y=x(x+2)(x-1)

• y=x(x-2)(x+1)

• y=-3x(x+2)(x-1)

• y=-2x(x-2)(x+1)

Which statements are true? Select two.

• A root with a multiplicity of 3 will result in a plateau point.

• A root with an even multiplicity will cross the x-axis.

• The function values of an even degree polynomial with a positive leading coefficient will approach infinity as the x values get larger.

• Parabolas must cross or touch the x-axis.

How many relative max or mins can a 4th degree polynomial have at most? (Hint #1: It might help to draw an example.) (Hint #2: Remember that max and min values don't have to occur on the x-axis.)

• 5

• 4

• 3

• 1

A function, g(x), has a zero that is a plateau point, and zero that is a relative max, and a zero that is a relative min.  What is the smallest the degree of g(x) could be?

• 10

• 7

• 5

• 3

Which functions have a negative leading coefficient?

• A

• B

• C

• D

Suppose the graph shown is moved up two units. Which statements could be true for the resulting function?

• The equation of the new function could be y=(x-3)².

• The equation of the new function would have a negative leading coefficient.

• The equation of the new function would have an odd degree.

• The function would have a minimum value at x = 3.

In which functions can you quickly find the x-intercepts of their graphs?

• y = 3x² - 2

• y = 5 - 2x + 3x² + 6x³

• y = 2x(x-4)(x+1)

• y = -3(x+1)(x-5)

Which of the following is NOT a solution to f(x)=3x(x-8)(2x+1)²?

• 0

• -1/2

• 1/2

• 8