Polynomial Functions Quiz

What is a polynomial function?

• A function involving only non-negative integer powers of x

• A function involving square roots

• A function involving division by x

• A function involving trigonometric functions

Which of the following functions are polynomial functions?

• f(x) = 12 - 4x^5 + 3x^2

• f(x) = 3x^3 - 2x + √x

• f(x) = 4x^2 + 2

• f(x) = sin(x) + 1

Write down one example of each of the following types of polynomial function:

• quartic, cubic, linear, quadratic

• quadratic, linear, cubic, quartic

• quadratic, cubic, linear, quartic

• cubic, linear, quartic, quadratic

Sketch the graphs of the following functions on the same axes:

• f(x) = -x^2

• f(x) = 4x^2

• f(x) = -4x^2

• f(x) = x^2

Consider a function of the form f(x) = x^2 + ax. When a > 0, what happens to the parabola as a increases?

• Moves down and to the right

• Moves up and to the left

• Moves up and to the right

• Moves down and to the left

Write down the maximum number of turning points on the graph of a polynomial function of degree:

• 2

• 3

• 12

• n

Write down a polynomial function with roots:

• 1, 2, 3, 4, 5

• 12, -1, -6

• 2, -4

• 1, 2, 3, 4

Write down the roots and identify their multiplicity for each of the following functions:

• (x-1)^2(x+3)

• (x-2)^2(x+1)

• (x-1)(x+2)^2(x-4)^3

• (x-2)^3(x+4)^4

Sketch the following functions:

• (x-1)^2(x+3)

• (x-2)^2(x+1)