Flash Lesson Monday 05.01.23 End Behavior Polynomial Functions

Front

What is the end behavior of a polynomial function?

Back

The end behavior of a polynomial function describes how the function behaves as x approaches positive or negative infinity.

Front

How does the degree of a polynomial affect its end behavior?

Back

The degree of a polynomial determines the number of times the graph can turn, influencing whether the ends of the graph go up or down.

Front

What role does the leading coefficient play in determining end behavior?

Back

The sign of the leading coefficient (positive or negative) affects whether the ends of the graph rise or fall.

Front

What is the end behavior of the polynomial f(x) = 2x^3 - x + 5?

Back

Left down & Right up.

Front

What is the degree of the polynomial f(x) = 2x^3 - x + 5?

Back

The degree is 3 (odd).

Front

What is the leading coefficient of the polynomial f(x) = 2x^3 - x + 5?

Back

The leading coefficient is 2 (positive).

Front

Classify the function f(x) = 2x^3 - x + 5.

Back

Cubic.

Front

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

Back

Both ends of the graph rise (x → ∞, y → ∞ and x → -∞, y → ∞).

Front

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

Back

Left up & Right down (x → -∞, y → ∞ and x → ∞, y → -∞).

Front

What does it mean if a polynomial has a leading coefficient that is a negative real number?

Back

It indicates that the right end of the graph will fall as x approaches positive infinity.