Symmetry with Odd and Even Functions

Front

What does the degree of a polynomial function indicate about its end behavior?

Back

The degree of a polynomial function indicates the direction in which the graph will rise or fall as x approaches positive or negative infinity.

Front

How does the sign of the leading coefficient affect the end behavior of a polynomial function?

Back

If the leading coefficient is positive, the graph rises to the right; if it is negative, the graph falls to the right.

Front

What is the definition of an odd function?

Back

An odd function is a function that exhibits symmetry about the origin, meaning f(-x) = -f(x) for all x in the domain.

Front

What is the definition of an even function?

Back

An even function is a function that exhibits symmetry about the y-axis, meaning f(-x) = f(x) for all x in the domain.

Front

How can you determine if a polynomial function is odd or even?

Back

To determine if a polynomial function is odd or even, check the exponents of the terms: if all exponents are even, it is even; if all exponents are odd, it is odd; if there are both, it is neither.

Front

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

Back

As x approaches positive infinity, y approaches positive infinity; as x approaches negative infinity, y approaches negative infinity.

Front

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

Back

As x approaches positive infinity, y approaches negative infinity; as x approaches negative infinity, y approaches positive infinity.

Front

What does it mean for a function to exhibit symmetry over the origin?

Back

It means that for every point (x, y) on the graph, the point (-x, -y) is also on the graph.

Front

Can a polynomial function be both even and odd?

Back

No, a polynomial function cannot be both even and odd. It can only be one or the other, or neither.

Front

What is the significance of the leading coefficient in determining the end behavior of polynomial functions?

Back

The leading coefficient determines whether the graph rises or falls at the ends, influencing the overall shape of the graph.