4-3 Attributes and Transformations of Rational Functions

Front

What is the parent function of rational functions?

Back

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

Front

What does it mean to shift a function right by 9 units?

Back

Shifting a function right by 9 units means to replace x with (x - 9) in the function's equation.

Front

What does it mean to shift a function up by 2 units?

Back

Shifting a function up by 2 units means to add 2 to the function's output, resulting in f(x) + 2.

Front

What is the domain of the function f(x) = 1/x?

Back

The domain of f(x) = 1/x is all real numbers except x = 0.

Front

What is the range of the function f(x) = 1/x?

Back

The range of f(x) = 1/x is all real numbers except y = 0.

Front

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

Back

The vertical asymptote is found by setting the denominator equal to zero and solving for x.

Front

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

Back

The horizontal asymptote can be found by analyzing the degrees of the numerator and denominator.

Front

What is the effect of a negative sign in front of a rational function?

Back

A negative sign in front of a rational function reflects the graph across the x-axis.

Front

What is the transformation of f(x) = 1/x when it is written as f(x) = 1/(x-9) + 2?

Back

This transformation shifts the graph right by 9 units and up by 2 units.

Front

What is the domain of the function f(x) = 1/(x+3)?

Back

The domain is all real numbers except x = -3.