End behavior of rational functions

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Graph the rational function given below. f (x) = (x2 - x - 2) / (x - 2) Solution : Step 1 : First, we have to find hole, if any. To find hole of the rational function, we have to see whether there is any common factor found at both numerator and denominator. So, let us factor both numerator and denominator. y = [ (x - 2) (x + 1)] / (x - 2) In ...

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Rational - 3. Irrational - 4. Not a Real Number - 5. \answer \sage a n s w e r 3. While many students have learned Irrational numbers are "Never ending, non-repeating decimals", this can be tricky with a calculator. A number like 3 / 17 may look Irrational if put in a calculator, but it does end after 16 places.Polynomials - End Behavior Describe the end behavior of each function. 1) f (x) = x3 + 10 x2 + 32 x + 34 f (x) → −∞ as x → −∞ f (x) → +∞ as x → +∞ 2) f (x) = −x2 − 8x − 15 f (x) → −∞ as x → −∞ f (x) → −∞ as x → +∞ 3) f (x) = −x4 + x2 + 2 f (x) → −∞ as x → −∞ f (x) → −∞ as x ...

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In addition, from the behavior of simple rational power functions such as \(\frac{1}{x}\text{,}\) we expect that rational functions may not only have horizontal asymptotes (as investigated in Section 5.4), but also vertical asymptotes. At first glance, these questions about zeros and vertical asymptotes of rational functions may appear to be ...

Module 1 – Polynomial, Rational, and Radical Relationships 3. a. What type of function is given on the right? b. What is the equation of the function? 4. a. Describe what happened to the parent function for the graph at the right. b. What is the equation of the function? c. Write the equation in standard form. d.