3.2 Sketching Graphs of Polynomials

Front

What does it mean if the graph of a function touches the x-axis?

Back

The zero has an even multiplicity.

Front

What are the roots of the polynomial function y = (x + 2)(x - 7)^3?

Back

-2, 7 (multiplicity 3)

Front

What effect do odd multiplicities have on the x-axis?

Back

They cross the x-axis.

Front

What is the end behavior of the polynomial y = 3(x + 4)^2(x + 1)(x - 3)^2?

Back

Falls to the left and rises to the right.

Front

What is the end behavior of a polynomial that goes down on the left and up on the right?

Back

It is described as 'down-up'.

Front

What does the term 'multiplicity' refer to in polynomial functions?

Back

The number of times a particular root appears.

Front

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

Back

By analyzing the leading term and its degree.

Front

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

Back

It determines the direction of the graph as x approaches infinity.

Front

What happens to the graph of a polynomial at a root with even multiplicity?

Back

The graph touches the x-axis and turns around.

Front

What happens to the graph of a polynomial at a root with odd multiplicity?

Back

The graph crosses the x-axis.