4.1, 4.2 summer

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where a function approaches infinity or negative infinity as the input approaches a. It indicates values that the function cannot take.

Tags

CCSS.HSF-IF.C.7D

Front

Identify the vertical asymptote of the function y = 3/x.

Back

The vertical asymptote is x = 0.

Tags

CCSS.HSF-IF.C.7D

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a line y = b where a function approaches the value b as the input approaches infinity or negative infinity.

Tags

CCSS.HSF-IF.C.7D

Front

Identify the horizontal asymptote of the function y = 3/x.

Back

The horizontal asymptote is y = 0.

Tags

CCSS.HSF-IF.C.7D

Front

What does the domain of a function represent?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Tags

CCSS.HSF.IF.A.1

CCSS.8.F.A.1

Front

What is the domain of the function y = 3/x?

Back

The domain is R except x = 0.

Front

What is the significance of the function's asymptotes?

Back

Asymptotes indicate the behavior of the function as it approaches certain values, helping to understand its graph.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find vertical asymptotes algebraically?

Back

Set the denominator of a rational function to zero and solve for x.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find horizontal asymptotes for rational functions?

Back

Compare the degrees of the numerator and denominator: If the degree of the numerator is less, y = 0; if equal, y = leading coefficient of numerator/leading coefficient of denominator.

Tags

CCSS.HSF-IF.C.7D

Front

What is the equation of the function with vertical asymptotes at x = 5 and x = -5?

Back

An example function is y = 1/(x^2 - 25).

Tags

CCSS.HSF-IF.C.7D