AP Precalculus Unit 1 Refresh

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where a function approaches infinity or negative infinity as x approaches a. It indicates values that the function cannot take.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a line y = b where a function approaches the value b as x approaches infinity or negative infinity. It indicates the end behavior of the function.

Front

How do you find vertical asymptotes of a rational function?

Back

Set the denominator of the rational function equal to zero and solve for x. The solutions are the vertical asymptotes.

Front

How do you find horizontal asymptotes of a rational function?

Back

Compare the degrees of the numerator and denominator: 1. If degree of numerator < degree of denominator, y = 0 is the horizontal asymptote. 2. If degrees are equal, y = leading coefficient of numerator / leading coefficient of denominator. 3. If degree of numerator > degree of denominator, there is no horizontal asymptote.

Front

What is the factored form of a polynomial with roots 2, 5i, and 6?

Back

Front

What does it mean for a function to be increasing on an interval?

Back

A function is increasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2 then f(x1) < f(x2).

Front

What does it mean for a function to be positive on an interval?

Back

A function is positive on an interval if f(x) > 0 for all x in that interval.

Front

What is the significance of the roots of a polynomial?

Back

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

Front

How do you determine the intervals where a function is positive or negative?

Back

Analyze the sign of the function in the intervals determined by its roots and vertical asymptotes. Test points in each interval to see if the function is positive or negative.

Front

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

Back

The degree of a polynomial determines its end behavior: 1. Even degree: both ends go in the same direction. 2. Odd degree: ends go in opposite directions.