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Today in Pre-Calculus

Today in Pre-Calculus. Notes: Rational Functions and Equations Transformations of the reciprocal function Go over quiz Homework. Rational Functions. A rational function, f(x) , is a ratio or quotient of polynomial functions p(x) and q(x) expressed as

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Today in Pre-Calculus

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  1. Today in Pre-Calculus • Notes: • Rational Functions and Equations • Transformations of the reciprocal function • Go over quiz • Homework

  2. Rational Functions A rational function, f(x), is a ratio or quotient of polynomial functions p(x) and q(x) expressed as * The domain of f(x) is all real numbers except where q(x) = 0

  3. Rational Functions yes. D:(-∞,0)υ(0,∞) Are the following rational functions? If yes, state the domain. yes. D: (-∞,∞) yes. D:(-∞,-2) υ (-2,2) υ (2,∞) No, numerator not a polynomial

  4. Transformations of the Reciprocal Function The simplest rational function is the basic function, Horizontal asymptote: y=0 Vertical asymptote: x=0

  5. Example 1 Sketch the graph and find an equation for the function g whose graph is obtained from the reciprocal function, by a translation of 2 units to the right.

  6. Example 2 Sketch the graph and find an equation for the function g whose graph is obtained from the reciprocal function, by a translation of 5 units to the right, followed by a reflection across the x-axis

  7. Example 3 Sketch the graph and find an equation for the function g whose graph is obtained from the reciprocal function, by a translation of 4 units to the left, followed by a vertical stretch by a factor of 3, and finally a translation 2 units down.

  8. Graphing Rational Functions The graph of any rational function of the form can be obtained by transforming If the degree of the numerator is greater than or equal to the degree of the denominator, we can use polynomial division to rewrite the rational function.

  9. Example 1 Vertical stretch: 3 Shift left 2

  10. Example 2 Reflect across x-axis Shift up 2

  11. Example 3 Vertical stretch: 8 Shift left 1 Shift down 3

  12. Homework • Pg. 245: 5-10 and 31-36 • Chapter 2 test: Tuesday, November 26

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