Exploring Characteristics of Polynomial Functions

This video tutorial explores the characteristics of polynomial functions using the example of X cubed plus 6 times x squared plus 8x. It covers identifying turning points, analyzing graph behavior, determining the parent function, and understanding end behavior. The tutorial also explains how to find zeros, domain, and range of the function.

What is the given polynomial function in the video?

• X^3 + 6X^2 + 8X

• X^2 + 6X^2 + 8X

• X^2 + 6X + 8

• X^3 + 6X + 8

What are the turning points of the given polynomial function?

• Relative Max at (-3, 3) and Relative Min at (-1, -3)

• Relative Max at (-1, -3) and Relative Min at (-3, 3)

• Relative Max at (3, -3) and Relative Min at (1, 3)

• Relative Max at (1, 3) and Relative Min at (3, -3)

In which intervals is the graph of the polynomial function increasing?

• From -3 to -1 and from -1 to infinity

• From -3 to infinity and from -1 to -infinity

• From -infinity to -3 and from -1 to infinity

• From -infinity to -1 and from -3 to infinity

What is the interval where the graph of the polynomial function is decreasing?

• From -1 to infinity

• From -infinity to -3

• From -1 to -3

• From -3 to -1

What is the parent function of the given polynomial function?

• f(x) = x^2

• f(x) = x^4

• f(x) = x^3

• f(x) = x

As x approaches infinity, what happens to the function?

• It remains constant

• It approaches positive infinity

• It oscillates

• It approaches negative infinity

Where does the function approach as x approaches negative infinity?

• It remains constant

• Zero

• Negative infinity

• Positive infinity

How many zeros does the polynomial function have?

• Three

• Four

• Two

• One

What are the x-values of the zeros of the polynomial function?

• -4, -2, 0

• -3, -1, 1

• -2, 0, 2

• -1, 1, 3

What is the domain of the polynomial function?

• Only integers

• Only negative numbers

• Only positive numbers

• All real numbers