10/21-FLASHCARD (Polynomial graph behavior)

Front

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

Back

As x → +∞, f(x) → +∞ and as x → -∞, f(x) → +∞.

Front

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

Back

As x → +∞, f(x) → -∞ and as x → -∞, f(x) → -∞.

Front

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

Back

As x → +∞, f(x) → +∞ and as x → -∞, f(x) → -∞.

Front

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

Back

As x → +∞, f(x) → -∞ and as x → -∞, f(x) → +∞.

Front

What does the leading coefficient of a polynomial determine?

Back

The leading coefficient determines the end behavior of the polynomial graph.

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 degree of a polynomial?

Back

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

Front

How do you determine the number of turning points in a polynomial graph?

Back

The maximum number of turning points is one less than the degree of the polynomial.

Front

What is a turning point in a polynomial graph?

Back

A turning point is a point where the graph changes direction from increasing to decreasing or vice versa.

Front

What is the significance of the y-intercept in a polynomial graph?

Back

The y-intercept is the value of the function when x = 0, indicating where the graph crosses the y-axis.