M3 Unit 4 Rational Functions EOC Review

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

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

Back

To find the horizontal asymptote, compare the degrees of 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{leading coefficient of numerator}{leading coefficient of denominator}.

Front

What is the x-intercept of a function?

Back

The x-intercept of a function is the point where the graph of the function crosses the x-axis, which occurs when f(x) = 0.

Front

How do you factor the expression 17xy - x?

Back

The expression can be factored as x(17y - 1).

Front

What is the process to multiply rational expressions?

Back

To multiply rational expressions, multiply the numerators together and the denominators together, then simplify if possible.

Front

What does it mean for a function to be undefined?

Back

A function is undefined at points where the denominator equals zero, as division by zero is not possible.

Front

How do you solve the equation \frac{1}{x-8} + \frac{1}{x^2+x-72} = \frac{6}{x-8}?

Back

To solve, find a common denominator, combine the fractions, and isolate x. The solution is x = -\frac{44}{5}.

Front

What is a vertical asymptote?

Back

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

Front

What is the significance of the leading coefficient in a rational function?

Back

The leading coefficient determines the end behavior of the function as x approaches positive or negative infinity.

Front

How do you determine if a rational expression can be simplified?

Back

A rational expression can be simplified if there are common factors in the numerator and denominator that can be canceled.