ALG.2: Unit 2 Lessons 16-22: Rational Functions B

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

Back

Front

What does the horizontal asymptote of a function indicate?

Back

The horizontal asymptote indicates the value that the function approaches as the input (x) approaches infinity or negative infinity.

Front

What happens to the average cost of t-shirts as you buy more?

Back

The average price/shirt will approach $3.25.

Front

Back

As the number of stickers (s) increases, the average cost per sticker approaches $3.

Front

How do you find vertical asymptotes of a rational function?

Back

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

Front

What is the significance of horizontal asymptotes in rational functions?

Back

Horizontal asymptotes indicate the end behavior of the function as x approaches infinity or negative infinity.

Front

What is the relationship between the degrees of the numerator and denominator in determining horizontal asymptotes?

Back

If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y=0. If they are equal, the horizontal asymptote is y = leading coefficient of numerator / leading coefficient of denominator.

Front

What is a rational function?

Back

A rational function is a function that can be expressed as the ratio of two polynomials.

Front

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

Back

If a function has no horizontal asymptote, it means that as x approaches infinity or negative infinity, the function does not approach a specific value.