End Behavior and Multiplicity

Front

What is end behavior in the context of polynomial functions?

Back

End behavior describes how the values of a function behave as the input (x) approaches positive or negative infinity.

Front

Define multiplicity in relation to polynomial roots.

Back

Multiplicity refers to the number of times a particular root (zero) appears in a polynomial function.

Front

What does it mean if a zero has an odd multiplicity?

Back

If a zero has an odd multiplicity, the graph of the function will cross the x-axis at that zero.

Front

What does it mean if a zero has an even multiplicity?

Back

If a zero has an even multiplicity, the graph of the function will touch the x-axis at that zero but will not cross it.

Front

How can you determine the end behavior of a polynomial function?

Back

The end behavior can be determined by the leading term of the polynomial and its degree.

Front

Back

Front

Back

The degree is 3.

Front

If a polynomial function has a leading coefficient greater than zero and an odd degree, what is its end behavior?

Back

As x approaches -∞, f(x) approaches -∞; as x approaches +∞, f(x) approaches +∞.

Front

If a polynomial function has a leading coefficient less than zero and an even degree, what is its end behavior?

Back

As x approaches -∞, f(x) approaches -∞; as x approaches +∞, f(x) approaches -∞.

Front

What is the significance of the x-intercepts of a polynomial function?

Back

The x-intercepts represent the roots of the function, where the function equals zero.