End Behavior & Zeros of Polynomials

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

What does the term 'zero' of a polynomial mean?

Back

A 'zero' of a polynomial is a value of x for which the polynomial evaluates to zero.

Front

What is the significance of the multiplicity of a zero?

Back

The multiplicity of a zero indicates how many times that zero is repeated in the polynomial. It affects the graph's behavior at that zero.

Front

What happens to the graph at a zero with odd multiplicity?

Back

The graph crosses the x-axis at a zero with odd multiplicity.

Front

What happens to the graph at a zero with even multiplicity?

Back

The graph bounces off the x-axis at a zero with even multiplicity.

Front

How do you determine the degree of a polynomial?

Back

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

Front

What is the end behavior of f(x) = -7x^3 + 2x - 1?

Back

As x → ∞, f(x) → -∞; As x → -∞, f(x) → ∞.

Front

How do you factor the polynomial f(x) = 4p³ + 8p² + 3p + 6?

Back

f(x) = (4p² + 3)(p + 2).

Front

What is the relationship between the degree of a polynomial and its end behavior?

Back

The degree of a polynomial determines the end behavior; odd degrees lead to opposite ends, while even degrees lead to the same end behavior.

Front

What is a polynomial function?

Back

A polynomial function is a function that can be expressed in the form f(x) = a_nx^n + a_(n-1)x^(n-1) + ... + a_1x + a_0, where a_n ≠ 0.