AP Precalculus Unit 1 Refresh

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What are vertical asymptotes?

Back

Vertical asymptotes are lines x = a where a function approaches infinity or negative infinity as x approaches a.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a line y = b that a function approaches as x approaches infinity or negative infinity.

Front

How do you find the intervals where a function is increasing?

Back

A function is increasing on intervals where its derivative is positive.

Front

What does it mean for a function to be positive?

Back

A function is positive on an interval if its output values (y-values) are greater than zero for all x in that interval.

Front

What is the significance of the point where a function changes from increasing to decreasing?

Back

This point is called a local maximum or minimum, indicating a change in the direction of the function.

Front

What is the difference between a local maximum and a global maximum?

Back

A local maximum is the highest point in a specific interval, while a global maximum is the highest point over the entire domain.

Front

How do you determine the vertical asymptotes of a rational function?

Back

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

Front

What is the relationship between the degree of the numerator and denominator in determining horizontal asymptotes?

Back

If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0. If they are equal, the asymptote is y = leading coefficient of numerator / leading coefficient of denominator.