Exploring Polynomials: End Behavior and Turning Points

What is a polynomial function?

• A function with coefficients multiplying power functions with negative exponents.

• A function with coefficients multiplying power functions with fractional exponents.

• A function with coefficients multiplying power functions with irrational exponents.

• A function with coefficients multiplying power functions with whole number exponents.

In standard form, how are the terms of a polynomial arranged?

• From the smallest exponent to the largest exponent.

• In any random order.

• From the largest exponent to the smallest exponent.

• From the middle exponent to the largest exponent.

What is the degree of the polynomial f(x) = 3x^4 + 2x^3 - x + 7?

• 1

• 2

• 3

• 4

What is the classification of a polynomial with degree 3?

• Quadratic

• Quintic

• Quartic

• Cubic

How does the end behavior of a polynomial with an even degree and a positive leading coefficient look?

• Both ends go up.

• Both ends go down.

• One end goes up and the other goes down.

• One end goes down and the other goes up.

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

• Both ends go up.

• Both ends go down.

• Starts low and goes high.

• Starts high and goes low.

For the polynomial -2x^5, what is the end behavior?

• As x moves to negative infinity, f(x) moves down; as x moves to positive infinity, f(x) moves up.

• As x moves to negative infinity, f(x) moves up; as x moves to positive infinity, f(x) moves down.

• Both ends go up.

• Both ends go down.

What is the end behavior of the polynomial 6x^2?

• One end goes up and the other goes down.

• One end goes down and the other goes up.

• Both ends go down.

• Both ends go up.

What is a turning point in a polynomial function?

• A point where the function is constant.

• A point where the function is undefined.

• A point where the function changes direction.

• A point where the function has a gap.

What do we call the highest point in a local region of a polynomial function?

• Absolute minimum

• Relative minimum

• Relative maximum

• Absolute maximum