Rational and Radical Functions

Vocabulary

asymptote

line that a graph approaches as one of the variables approaches infinity or negative infinity

extraneous solution

solution of a step in solving that is not a solution of the original equation

hole

missing value in a graph such that the graph approaches the same value on both sides

inverse variation

relationship for variables xx and yy and constant kk that can be written as:
y=kxy = \frac{k}{x}

multiplicity

If xcx-c is a factor of a polynomial function, the multiplicity of the zero x=cx=c is the number of times that the factor appears, or the exponent of the factor.

radical function

function whose rule can be written using an expression with a variable under a root, such as a square root or cube root:
f(x)=p(x)nf(x)=\sqrt[\scriptsize{n}]{p(x)}

rational function

function whose rule can be expressed as a fraction of two polynomials:
f(x)=p(x)q(x)f(x)=\frac{p(x)}{q(x)}

reciprocal function

function in the form:
f(x)=1xf(x)=\frac{1}{x}