Rational Function Transformations

Front

What is a rational function?

Back

A rational function is a function that can be expressed as the quotient of two polynomials, typically in the form f(x) = P(x)/Q(x), where P and Q are polynomials.

Front

What is the parent function of rational functions?

Back

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

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where the function approaches infinity or negative infinity as x approaches a.

Front

How does the graph of f(x) = 1/x change when we add a constant to the numerator?

Back

Adding a constant to the numerator shifts the graph vertically. For example, f(x) = 1/x + 3 shifts the graph up by 3 units.

Front

What is a horizontal asymptote?

Back

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

Front

How does the graph of f(x) = 1/x change when we add a constant to the denominator?

Back

Adding a constant to the denominator shifts the graph horizontally. For example, f(x) = 1/(x + 3) shifts the graph left by 3 units.

Front

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

Back

The domain is all real numbers except x = 3, or D: x ∈ ℝ, x ≠ 3.

Front

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

Back

The range is all real numbers except y = 0, or R: y ∈ ℝ, y ≠ 0.

Front

What happens to the graph of f(x) = 1/x when x approaches 0?

Back

As x approaches 0, f(x) approaches infinity or negative infinity, indicating a vertical asymptote at x = 0.

Front

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

Back

A negative sign reflects the graph across the x-axis. For example, f(x) = -1/x reflects the graph of f(x) = 1/x.