Think of the result of multiplying the factors together. To find the horizontal asymptotes, check the degrees of the numerator and denominator. The vertical asymptotes are x = −2, x = 1, and x = 3. Since it is factored, set each factor equal to zero and solve. Notice that there are no common factors between the numerator and denominator, so there are no removable discontinuities.įind the vertical asymptotes by setting the denominator equal to zero and solving for x. SolutionĬonveniently, this is already factored. Rational functions then are functions written as fractions of polynomial functions in the form \(f(x) = \frac\). In mathematics, rational means "ratio" or can be written as a fraction. Rational functions are like the one above in the introduction. This lesson is about rational functions which have variables in the denominator. The last few lessons have been about polynomial functions which have non-negative integers for exponents. Written without a variable in the denominator, this function will contain a negative integer power. Many other applications require finding averages in a similar way. The average cost function for this situation is The average cost for producing x items is found by dividing the cost function by the number of items, x. This indicates that each item costs $125 and there is a $2000 initial cost to setup the production floor. In a particular factory, the cost is given by the equation C( x) = 125 x + 2000. In factories, the cost of making a product is dependent on the number of items, x, produced. Find the domains of rational functions.įigure 1: Factory floor (credit pixabay/Tama66).
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