Review Unit 6 Rational Functions:

Front

What is a rational function?

Back

A rational function is a function that can be expressed as the quotient of two polynomials, where the denominator is not zero.

Front

What is the vertical asymptote of a rational function?

Back

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

Front

How do you find the vertical asymptote of the function y = (x-2)/(x+5)?

Back

Set the denominator equal to zero: x + 5 = 0, which gives x = -5.

Front

What is the x-intercept of a function?

Back

The x-intercept is the point where the graph of the function crosses the x-axis, found by setting y = 0.

Front

How do you find the x-intercept of the function y = (x-3)/(x-5)?

Back

Set the numerator equal to zero: x - 3 = 0, which gives x = 3.

Front

What is the domain of a rational function?

Back

The domain is the set of all real numbers except where the denominator is zero.

Front

What is a hole in a rational function?

Back

A hole occurs at a value of x where both the numerator and denominator are zero, indicating a removable discontinuity.

Front

How do you write a rational function with a vertical asymptote at x = 4?

Back

The denominator must include (x - 4) to create a vertical asymptote at x = 4.

Front

What is the significance of the degree of the numerator and denominator in a rational function?

Back

The degree determines the end behavior of the function and the presence of horizontal asymptotes.

Front

What is a horizontal asymptote?

Back

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