3.2 Pt.1 TOTD

Front

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

Back

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

Front

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

Back

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

Front

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

Back

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

Front

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

Back

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

Front

Define the degree of a polynomial.

Back

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

Front

What does a positive leading coefficient indicate about the end behavior of a polynomial function?

Back

A positive leading coefficient indicates that the function will rise to +∞ as x approaches +∞.

Front

What does a negative leading coefficient indicate about the end behavior of a polynomial function?

Back

A negative leading coefficient indicates that the function will fall to -∞ as x approaches +∞.

Front

How can you determine the degree of a polynomial from its graph?

Back

The degree can be determined by the number of turning points; a polynomial of degree n can have at most n-1 turning points.

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.

Front

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

Back

The leading term determines the end behavior of the polynomial function.