Understanding End Behavior of Power Functions

This video tutorial explores the end behavior of power functions, focusing on how the degree and leading coefficient affect the graph's behavior as x approaches positive or negative infinity. It covers four examples: two with even degrees and two with odd degrees, highlighting the differences in graph behavior based on whether the leading coefficient is positive or negative. The video concludes with a summary table to help visualize these concepts.

What happens to the graph of a function as x approaches negative infinity?

• The graph moves downwards.

• The graph moves upwards.

• The graph moves to the left.

• The graph moves to the right.

For the function f(x) = x^6, what is the end behavior as x approaches positive infinity?

• f(x) approaches negative infinity.

• f(x) approaches zero.

• f(x) approaches positive infinity.

• f(x) remains constant.

How does the end behavior of f(x) = -x^4 differ from f(x) = x^6?

• Both approach positive infinity.

• Both approach negative infinity.

• f(x) = -x^4 approaches negative infinity, while f(x) = x^6 approaches positive infinity.

• f(x) = -x^4 approaches positive infinity, while f(x) = x^6 approaches negative infinity.

What is the end behavior of f(x) = x^3 as x approaches negative infinity?

• f(x) approaches positive infinity.

• f(x) approaches zero.

• f(x) approaches negative infinity.

• f(x) remains constant.

For the function f(x) = -x^5, what happens as x approaches positive infinity?

• f(x) approaches negative infinity.

• f(x) approaches zero.

• f(x) remains constant.

• f(x) approaches positive infinity.

What is the general end behavior for power functions with an even degree and a positive leading coefficient?

• Both ends of the graph approach positive infinity.

• One end approaches positive infinity, the other negative infinity.

• Both ends of the graph approach negative infinity.

• The graph remains constant.

How does the end behavior change for power functions with an odd degree and a negative leading coefficient?

• Both ends approach positive infinity.

• The graph remains constant.

• Both ends approach negative infinity.

• One end approaches positive infinity, the other negative infinity.

Which of the following is true for power functions with an odd degree and a positive leading coefficient?

• One end approaches positive infinity, the other negative infinity.

• Both ends approach negative infinity.

• Both ends approach positive infinity.

• The graph remains constant.

What is the significance of the leading coefficient in determining the end behavior of power functions?

• It determines the degree of the function.

• It affects the direction of the graph's end behavior.

• It has no effect on the end behavior.

• It only affects the graph's shape, not the end behavior.

Which column should you look at in the summary table if the degree of the power function is odd?

• The column for odd degrees.

• The column for positive coefficients.

• The column for negative coefficients.

• The column for even degrees.