Transformations of Rational Functions

Front

What is a vertical asymptote?

Back

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

Front

What are the asymptotes of the function g(x) = 4 / (x - 5)?

Back

The asymptotes are x = 5 (vertical asymptote) and y = 0 (horizontal asymptote).

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a line y = b that a function approaches as x approaches infinity or negative infinity. It indicates the end behavior of the function.

Front

What transformation occurs when the function g(x) = 1/x is shifted right by 5 units?

Back

The new function is g(x) = 1/(x - 5).

Front

What transformation occurs when the function g(x) = 1/x is shifted up by 7 units?

Back

The new function is g(x) = 1/x + 7.

Front

What does it mean to reflect a function over the x-axis?

Back

Reflecting a function over the x-axis means to multiply the function by -1, changing the sign of the output values.

Front

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

Back

Set the denominator equal to zero and solve for x. The values of x that make the denominator zero are the vertical asymptotes.

Front

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

Back

For rational functions, 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 the parent function of rational functions?

Back

The parent function of rational functions is g(x) = 1/x.

Front

What happens to the graph of a rational function as x approaches a vertical asymptote?

Back

The graph will approach infinity or negative infinity, indicating that the function is undefined at that point.