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.

Front

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

Back

The vertical asymptote is x = 0.

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.

Front

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

Back

The horizontal asymptote is y = 0.

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.

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.

Front

How do you find vertical asymptotes algebraically?

Back

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

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.

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).