PreCalculus 1.1 - 1.3 Flashcard Review

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. For example, the range of the function f(x) = x^2 is [0, ∞) because the output is always non-negative.

Front

What does it mean for a function to be CONTINUOUS at a point?

Back

A function is CONTINUOUS at a point x = a if the following three conditions are met: 1) f(a) is defined, 2) the limit of f(x) as x approaches a exists, and 3) the limit equals f(a).

Front

What are VERTICAL ASYMPTOTES?

Back

Vertical asymptotes are lines x = a where a function approaches infinity or negative infinity as x approaches a. They occur in rational functions where the denominator is zero.

Front

How can you determine if a function is EVEN?

Back

A function f(x) is considered EVEN if f(-x) = f(x) for all x in the domain. This means the graph of the function is symmetric about the y-axis.

Front

What is the range of the function f(x) = x^2?

Back

The range of the function f(x) = x^2 is [0, ∞) because the output values are always non-negative.

Front

What is a REMOVABLE DISCONTINUITY?

Back

A removable discontinuity occurs at a point where a function is not defined, but can be made continuous by defining or redefining the function at that point.

Front

What is an INFINITE DISCONTINUITY?

Back

An infinite discontinuity occurs when the function approaches infinity or negative infinity as x approaches a certain value, typically seen in rational functions.

Front

What is a JUMP DISCONTINUITY?

Back

A jump discontinuity occurs when the left-hand limit and right-hand limit at a point are not equal, causing a 'jump' in the graph of the function.

Front

What is the definition of an ASYMPTOTE?

Back

An asymptote is a line that a graph approaches but never touches. There are vertical, horizontal, and oblique asymptotes.

Front

What is the difference between the DOMAIN and RANGE of a function?

Back

The DOMAIN of a function is the set of all possible input values (x-values), while the RANGE is the set of all possible output values (y-values).