Exploring Graph Polynomials and Their End Behavior

The video tutorial covers graphing polynomials, focusing on a cubic function. It explains how to evaluate and plot points, and discusses the end behavior of polynomial graphs. The tutorial also explores patterns in end behavior based on the degree and leading coefficient of polynomials.

What is the range of x-values recommended for graphing the polynomial function?

• Negative 2 to 2

• Negative 10 to 10

• Negative 3 to 3

• Negative 5 to 5

What is the first step in evaluating the polynomial function for a given x-value?

• Multiply the x-value by 3

• Cube the x-value

• Square the x-value

• Add 3 to the x-value

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CCSS.HSF.IF.A.2

What is the result of evaluating the polynomial function at x = -3?

• 24

• 0

• 27

• 9

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CCSS.HSF.IF.A.2

What is the final value of the polynomial function at x = -2 using synthetic substitution?

• 12

• 9

• 6

• 3

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CCSS.HSF.IF.A.2

Which point is plotted at x = 0 on the graph?

• (0, -1)

• (0, 3)

• (0, -3)

• (0, 0)

How many sections does a cubic graph function typically have?

• One

• Two

• Four

• Three

What happens to the graph of a polynomial function with an odd degree and a positive leading coefficient as x approaches positive infinity?

• The graph goes to negative infinity

• The graph oscillates

• The graph stays constant

• The graph goes to positive infinity

What is the end behavior of a polynomial function with an even degree and a negative leading coefficient?

• The graph stays constant

• One end goes to positive infinity and the other to negative infinity

• Both ends go to negative infinity

• Both ends go to positive infinity

For a polynomial function with an even degree and a positive leading coefficient, what happens as x approaches negative infinity?

• The graph goes to positive infinity

• The graph goes to negative infinity

• The graph oscillates

• The graph stays constant

What is the degree and leading coefficient of a polynomial function if both ends of the graph go to negative infinity?

• Even degree, positive leading coefficient

• Odd degree, negative leading coefficient

• Even degree, negative leading coefficient

• Odd degree, positive leading coefficient