AP PreCalculus Unit 1 Review

Front

Define end behavior of a polynomial function.

Back

The end behavior of a polynomial function describes the behavior of the function as the input values approach positive or negative infinity. It is determined by the leading term of the polynomial.

Front

What does it mean for a function to have a hole in its graph?

Back

A hole in the graph of a function occurs at a point where the function is not defined due to a factor that cancels out in the function's expression, indicating a removable discontinuity.

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where a function approaches infinity or negative infinity as the input approaches a. It indicates that the function is undefined at that point.

Front

How do you determine the degree of a polynomial?

Back

Front

What is a slant (oblique) asymptote?

Back

A slant asymptote occurs when the degree of the numerator is one higher than the degree of the denominator in a rational function. It can be found using polynomial long division.

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Back

Front

What is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient determines the direction of the end behavior of the polynomial function. If it is positive, the function rises to positive infinity as x approaches positive infinity; if negative, it falls to negative infinity.

Front

Explain the concept of a rational function.

Back

Front

What is the relationship between the degree of a polynomial and its end behavior?

Back

The degree of a polynomial influences its end behavior. Even-degree polynomials have the same end behavior (both up or both down), while odd-degree polynomials have opposite end behaviors (one up, one down).

Front

How do you find the horizontal asymptote of a rational function?

Back