Math 3 Unit 3 Test Polynomials and Rational Functions

Front

What is the degree of a polynomial function?

Back

The degree of a polynomial function is the highest power of the variable in the polynomial. It determines the function's end behavior and the number of roots.

Front

What does it mean for a polynomial function to be even or odd?

Back

An even polynomial function has all even degree terms and is symmetric about the y-axis. An odd polynomial function has all odd degree terms and is symmetric about the origin.

Front

What is end behavior in the context of polynomial functions?

Back

End behavior describes how the values of a function behave as the input approaches positive or negative infinity.

Front

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

Back

The end behavior can be determined by the leading term of the polynomial. If the leading coefficient is positive and the degree is even, both ends go up. If the degree is odd, one end goes up and the other goes down.

Front

What are zeros of a polynomial?

Back

Zeros of a polynomial are the values of x for which the polynomial equals zero. They represent the x-intercepts of the graph.

Front

How do you write a polynomial given its zeros?

Back

To write a polynomial given its zeros, use the factored form: if the zeros are a, b, and c, the polynomial can be expressed as (x-a)(x-b)(x-c).

Front

What are asymptotes in rational functions?

Back

Asymptotes are lines that the graph of a function approaches but never touches. They can be vertical, horizontal, or oblique.

Front

How do you find vertical asymptotes of a rational function?

Back

Vertical asymptotes occur at the values of x that make the denominator zero, provided those values do not also make the numerator zero.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity.

Front

How do you determine horizontal asymptotes for rational functions?

Back

To find horizontal asymptotes, compare the degrees of the numerator and denominator. If the degree of the numerator is less, y=0; if equal, y= leading coefficient of numerator/leading coefficient of denominator; if greater, no horizontal asymptote.