Unit 4B Skills Check - End Behavior

Front

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

Back

As x → ∞, f(x) → ∞ and as x → -∞, f(x) → ∞.

Front

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

Back

As x → ∞, f(x) → ∞ and as x → -∞, f(x) → -∞.

Front

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

Back

As x → ∞, f(x) → -∞ and as x → -∞, f(x) → ∞.

Front

What does the leading coefficient of a polynomial function determine?

Back

The leading coefficient determines the end behavior of the polynomial function.

Front

How can you identify the degree of a polynomial function?

Back

The degree of a polynomial function is the highest power of the variable in the polynomial.

Front

What is the significance of the leading term in a polynomial function?

Back

The leading term influences the end behavior of the polynomial as x approaches positive or negative infinity.

Front

What is the general form of a cubic polynomial?

Back

A cubic polynomial is generally expressed as f(x) = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants.

Front

What is the difference between even and odd degree polynomials in terms of symmetry?

Back

Even degree polynomials are symmetric about the y-axis, while odd degree polynomials have rotational symmetry about the origin.

Front

What is the end behavior of the function f(x) = -3x^3 + 2x - x^4?

Back

As x → ∞, f(x) → -∞ and as x → -∞, f(x) → -∞.

Front

What type of polynomial has a degree of 4?

Back

A polynomial with a degree of 4 is called a quartic polynomial.