Precalc. AB Semester Final Part 2

Front

What is the definition of a decreasing function?

Back

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

Front

What is an asymptote in the context of rational functions?

Back

An asymptote is a line that a graph approaches but never touches. Vertical asymptotes occur where the function is undefined, and horizontal asymptotes describe the end behavior of the function.

Front

How do you find the domain of a logarithmic function?

Back

Front

What is the formula for the average rate of change of a function?

Back

Front

What is the end behavior of a polynomial function?

Back

The end behavior of a polynomial function is determined by its leading term. As x approaches infinity or negative infinity, the function will approach the value of the leading term.

Front

What is the difference between a vertical and horizontal asymptote?

Back

A vertical asymptote indicates where a function approaches infinity (or negative infinity) as x approaches a certain value, while a horizontal asymptote indicates the value that f(x) approaches as x approaches infinity or negative infinity.

Front

How do you determine the intervals of increase and decrease for a function?

Back

To determine intervals of increase and decrease, find the derivative of the function. If the derivative is positive on an interval, the function is increasing; if negative, it is decreasing.

Front

What is the significance of the limit in calculus?

Back

Limits are used to define continuity, derivatives, and integrals. They describe the behavior of functions as they approach a certain point.

Front

What is the definition of a rational function?

Back

Front

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

Back

The end behavior of a polynomial function is determined by the degree and the leading coefficient. An even degree with a positive leading coefficient will rise on both ends, while an odd degree will rise on one end and fall on the other.