11 x1 t15 02 sketching polynomials (2013)

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11 x1 t15 02 sketching polynomials (2013)

  1. 1. Sketching Polynomials When drawing y = P(x) • y intercept is the constant
  2. 2. e.g. y   x  1 x  1  x  2  3 2  y     x             
  3. 3. Sketching Polynomials When drawing y = P(x) • y intercept is the constant • x intercepts are the roots
  4. 4. e.g. y   x  1 x  1  x  2  3 2  y     x             
  5. 5. Sketching Polynomials When drawing y = P(x) • y intercept is the constant • x intercepts are the roots • as x   , P(x) acts like the leading term
  6. 6. e.g. y   x  1 x  1  x  2  3 2  y     x             
  7. 7. e.g. y   x  1 x  1  x  2  3 2  graph starts here y     x             
  8. 8. e.g. y   x  1 x  1  x  2  3 2  graph starts here y graph finishes here     x             
  9. 9. Sketching Polynomials When drawing y = P(x) • y intercept is the constant • x intercepts are the roots • as x   , P(x) acts like the leading term • even powered roots look like or
  10. 10. e.g. y   x  1 x  1  x  2  3 2  graph starts here y graph finishes here     x             
  11. 11. Sketching Polynomials When drawing y = P(x) • y intercept is the constant • x intercepts are the roots • as x   , P(x) acts like the leading term • even powered roots look like or • odd powered roots look like or
  12. 12. e.g. y   x  1 x  1  x  2  3 2  graph starts here y graph finishes here     x             
  13. 13. e.g. y   x  1 x  1  x  2  3 2  y     x             
  14. 14. Sketching Polynomials When drawing y = P(x) • y intercept is the constant • x intercepts are the roots • as x   , P(x) acts like the leading term • even powered roots look like or • odd powered roots look like or • If the polynomial can be written as  x  a  , then it is a basic curve n
  15. 15. e.g. y   x  1  x  1  x  2   x  2  4 3 2
  16. 16. e.g. y   x  1  x  1  x  2   x  2  4 3 2 y  x        
  17. 17. Exercise 4B; 3cei, 4deghi, 6acm 7ac, 8, 11

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