HW 15 - Ch 2.6 Homework(PC)

Front

What is a horizontal asymptote?

Back

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

Tags

CCSS.HSF-IF.C.7D

Front

How do you determine the horizontal asymptote of a rational function?

Back

For rational functions, the horizontal asymptote can be determined by comparing the degrees of the numerator and denominator. 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 asymptote is y = (leading coefficient of numerator)/(leading coefficient of denominator). If the degree of the numerator is greater, there is no horizontal asymptote.

Tags

CCSS.HSF-IF.C.7D

Front

What is a vertical asymptote?

Back

A vertical asymptote is a vertical line that the graph of a function approaches as the input approaches a certain value, typically where the function is undefined.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find vertical asymptotes in a rational function?

Back

Vertical asymptotes can be found by setting the denominator of a rational function equal to zero and solving for x.

Tags

CCSS.HSF-IF.C.7D

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 positive or negative infinity, the function does not approach a specific y-value.

Tags

CCSS.HSF-IF.C.7D

Front

What is the significance of the leading coefficient in determining horizontal asymptotes?

Back

The leading coefficient of the numerator and denominator helps determine the value of the horizontal asymptote when the degrees of the numerator and denominator are equal.

Tags

CCSS.HSF-IF.C.7D

Front

Can a function have both vertical and horizontal asymptotes?

Back

Yes, a function can have both vertical and horizontal asymptotes. Vertical asymptotes occur where the function is undefined, while horizontal asymptotes describe the behavior of the function as x approaches infinity.

Tags

CCSS.HSF-IF.C.7D

Front

What is the relationship between asymptotes and the graph of a function?

Back

Asymptotes indicate the behavior of the graph of a function as it approaches certain values, helping to understand the limits and overall shape of the graph.

Tags

CCSS.HSF-IF.C.7D

Front

Provide an example of a function with a horizontal asymptote at y = 2.

Back

An example is f(x) = (2x + 1)/(x + 1). As x approaches infinity, f(x) approaches 2.

Tags

CCSS.HSF-IF.C.7D

Front

Provide an example of a function with vertical asymptotes at x = 3 and x = -3.

Back

An example is f(x) = 1/(x^2 - 9). The function is undefined at x = 3 and x = -3.

Tags

CCSS.HSF-IF.C.7D