3.1-3.3 Review Honors Pre-Calculus (Polynomial Functions)

Front

State the zeros of the polynomial f(x) = x(x+3)²(x - 2).

Back

x = 0, -3 (multiplicity of 2), 2

Front

On what interval is the function f(x) decreasing?

Back

(−∞, −2.55) U (0, 2.55)

Front

Where is the function f(x) increasing?

Back

(4, ∞)

Front

Which function has the end behavior of a polynomial with a positive leading coefficient and even degree?

Back

x⁴ + 3x³ - 4x + 1

Front

Describe the behavior of the zeros at the x-axis for the polynomial with x-intercepts 1, -3, and -4.

Back

1 crosses, -3 touches, -4 touches

Front

What is the multiplicity of a zero?

Back

The multiplicity of a zero is the number of times that zero is repeated as a root of the polynomial.

Front

How do you determine if a polynomial function is increasing or decreasing on an interval?

Back

Analyze the first derivative of the function; if f'(x) > 0, the function is increasing; if f'(x) < 0, it is decreasing.

Front

What is the end behavior of a polynomial function?

Back

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

Front

What does it mean for a polynomial to have a zero of even multiplicity?

Back

A zero of even multiplicity means the graph touches the x-axis at that zero but does not cross it.

Front

What does it mean for a polynomial to have a zero of odd multiplicity?

Back

A zero of odd multiplicity means the graph crosses the x-axis at that zero.