Alg 2; Ch 8 1/8; Do Now

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where a function approaches infinity or negative infinity as x approaches a. It indicates that the function is undefined at that point.

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Back

x = -3

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a line y = b where a function approaches b as x approaches infinity or negative infinity. It indicates the behavior of the function at extreme values of x.

Front

Back

y = 0

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Back

Front

Back

The negative sign reflects the graph across the x-axis.

Front

Back

Vertical asymptote: x = -2; Horizontal asymptote: y = -5.

Front

How do you find the vertical asymptote of a rational function?

Back

Set the denominator equal to zero and solve for x.

Front

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

Back

It means the function is defined for all real numbers, and the denominator does not equal zero for any x.

Front

What is the significance of the point where a vertical asymptote occurs?

Back

It indicates a value of x where the function is undefined and where the function's behavior changes dramatically.