Applying and analysing functions

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line that a graph approaches but never touches or crosses. It occurs where the function is undefined, typically where the denominator of a rational function equals zero.

Front

How do you find vertical asymptotes in a rational function?

Back

To find vertical asymptotes, set the denominator of the rational function equal to zero and solve for the variable.

Front

What is the significance of vertical asymptotes in graphing functions?

Back

Vertical asymptotes indicate values where the function approaches infinity or negative infinity, helping to understand the behavior of the graph near those points.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as the input values approach positive or negative infinity.

Front

How do you determine horizontal asymptotes for rational functions?

Back

To find horizontal asymptotes, compare the degrees of the numerator and denominator. If the degree of the numerator is less, the asymptote is y=0. If they are equal, the asymptote is y= the ratio of the leading coefficients.

Front

What is the end behavior of a function?

Back

End behavior describes how the values of a function behave as the input approaches positive or negative infinity, often determined by horizontal asymptotes.

Front

What is the relationship between vertical asymptotes and the denominator of a function?

Back

Vertical asymptotes are determined by the values that make the denominator of a rational function equal to zero.

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What does it mean if a function has no vertical asymptotes?

Back

If a function has no vertical asymptotes, it means that the function is defined for all real numbers and does not approach infinity at any point.

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What is the difference between vertical and horizontal asymptotes?

Back

Vertical asymptotes are vertical lines where the function approaches infinity, while horizontal asymptotes are horizontal lines that the function approaches as the input goes to infinity.

Front

How can you identify the presence of an asymptote in a graph?

Back

Asymptotes can be identified in a graph by observing where the graph approaches a line but does not touch or cross it.