Question

Solve each problem. Work each of the following. Find an equation for a possible corresponding rational function.

Accepted Answer

Understand that a rational function is a function of the form $$f(x) = \frac{P(x)}{Q(x)}$$, where $$P(x)$$ and $$Q(x)$$ are polynomials and $$Q(x) 
eq 0. $$Identify the key features or conditions given in the problem (such as zeros, vertical asymptotes, horizontal asymptotes, or points the function must pass through) to determine the form of $$P(x)$$ and $$Q(x). $$Construct the numerator polynomial $$P(x)$$ using the zeros of the function. For example, if the function has zeros at $$x = a$$ and $$x = b$$, then $$P(x)$$ could include factors like $$(x - a)$$ and $$(x - b). $$Construct the denominator polynomial $$Q(x)$$ using the vertical asymptotes or restrictions on the domain. For example, if there is a vertical asymptote at $$x = c$$, then $$Q(x)$$ could include a factor like $$(x - c). $$Combine $$P(x)$$ and $$Q(x) to $$write the rational function $$f(x) = \frac{P(x)}{Q(x)}. $$Adjust coefficients if necessary to satisfy any additional conditions such as specific function values.

Solve each problem. Work each of the following. Find an equation for a possible corresponding rational function.

Verified video answer for a similar problem:

Key Concepts

Rational Functions

Domain and Restrictions

Constructing Rational Functions from Conditions