Front

What does it mean when a function goes up on the left?

Back

It means that as x approaches negative infinity (x → -∞), the value of y approaches positive infinity (y → ∞).

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. It determines the end behavior of the polynomial function.

Front

What does it mean when a function goes down on the left?

Back

It means that as x approaches negative infinity (x → -∞), the value of y approaches negative infinity (y → -∞).

Front

What is a root of a polynomial?

Back

A root of a polynomial is a value of x for which the polynomial equals zero.

Front

What is multiplicity in relation to roots?

Back

Multiplicity refers to the number of times a particular root appears in a polynomial. A root with an even multiplicity will touch the x-axis, while a root with an odd multiplicity will cross the x-axis.

Front

How do you identify the zeros of a polynomial function?

Back

To identify the zeros, set the polynomial equal to zero and solve for x.

Front

What is the significance of the leading coefficient being positive?

Back

If the leading coefficient is positive, the polynomial function will rise to positive infinity as x approaches positive infinity.

Front

What is the significance of the leading coefficient being negative?

Back

If the leading coefficient is negative, the polynomial function will fall to negative infinity as x approaches positive infinity.

Front

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

Back

The end behavior is determined by the leading term of the polynomial, specifically the leading coefficient and the degree of the polynomial.

Front

What does it mean for a root to have a multiplicity of 2?

Back

A root with a multiplicity of 2 means that it is a repeated root, and the graph will touch the x-axis at that point but not cross it.