Rational Function Test Review

Front

What is a rational function?

Back

Front

How do you simplify a rational expression?

Back

To simplify a rational expression, factor the numerator and denominator and then cancel any common factors.

Front

What is the horizontal asymptote of a rational function?

Back

The horizontal asymptote of a rational function is determined by the degrees of the polynomials in the numerator and denominator. If the degree of the numerator is less than the degree of the denominator, the asymptote is y=0. If they are equal, the asymptote is y=\frac{a}{b} where a and b are the leading coefficients.

Front

What is the vertical asymptote of a rational function?

Back

The vertical asymptote occurs at values of x that make the denominator zero, provided that these values do not also make the numerator zero.

Front

How do you find the product of two rational expressions?

Back

To find the product of two rational expressions, multiply the numerators together and the denominators together, then simplify the resulting expression.

Front

What does it mean to transform a function?

Back

Transforming a function involves shifting, reflecting, stretching, or compressing the graph of the function. Common transformations include vertical shifts, horizontal shifts, reflections, and dilations.

Front

What is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient of a polynomial determines the end behavior of the graph. It influences whether the graph rises or falls as x approaches positive or negative infinity.

Front

What is the difference between a removable and non-removable discontinuity?

Back

A removable discontinuity occurs when a factor cancels in a rational expression, while a non-removable discontinuity occurs at a vertical asymptote where the function is undefined.

Front

How do you determine if a function is increasing or decreasing?

Back

A function is increasing on an interval if its derivative is positive on that interval, and decreasing if its derivative is negative.

Front

What is the domain of a rational function?

Back

The domain of a rational function includes all real numbers except those that make the denominator zero.