Math 3 Flashcard #14 - S1

Front

Which root has even multiplicity?

Back

1

Front

Describe the end behavior of the function: y = -2x^2 - x + 14

Back

Falls to the left, Falls to the right.

Front

Describe the end behavior of the function: y = 5x^3 - 2x^2 + 4x - 3

Back

Falls to the left, Rises to the right.

Front

How many real zeros are shown in the graph?

Back

4

Front

What is the degree of f(x) = -3x^4 + x^3 - 2x^2 + x - 1?

Back

4

Front

What is the definition of a polynomial function?

Back

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, a_(n-1), ..., a_0 are constants and n is a non-negative integer.

Front

What is the leading coefficient of the polynomial f(x) = -3x^4 + x^3 - 2x^2 + x - 1?

Back

-3

Front

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

Back

The degree indicates the number of times the graph can turn and the direction it will go as x approaches positive or negative infinity.

Front

What is the significance of the roots of a polynomial function?

Back

The roots are the values of x for which f(x) = 0, indicating where the graph intersects the x-axis.

Front

What is the relationship between the multiplicity of a root and the behavior of the graph at that root?

Back

If a root has even multiplicity, the graph touches the x-axis at that root; if it has odd multiplicity, the graph crosses the x-axis.