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.

Tags

CCSS.HSF-IF.C.7D

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

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

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.

Tags

CCSS.HSF-IF.C.7D

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

Tags

CCSS.HSF-IF.C.7D

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.