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Warm Up Graph the function

Warm Up Graph the function. We have graphed several functions, now we are adding one more to the list! Graphing Rational Functions. Parent Function:. Pay attention to the transformation clues!. (-a indicates a reflection in the x-axis). a x – h. f(x) = + k.

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Warm Up Graph the function

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  1. Warm Up Graph the function

  2. We have graphed several functions, now we are adding one more to the list! Graphing Rational Functions

  3. Parent Function:

  4. Pay attention to the transformation clues! (-a indicates a reflection in the x-axis) a x – h f(x) = + k vertical translation (-k = down, +k = up) horizontal translation (+h = left, -h = right) Watch the negative sign!! If h = -2 it will appear as x + 2.

  5. Asymptotes • Places on the graph the function will approach, but will never touch.

  6. Graph: 1 x f(x) = Vertical Asymptote: x = 0 Horizontal Asymptote: y = 0 No horizontal shift. No vertical shift. A HYPERBOLA!!

  7. W look like?

  8. 1 x + 4 Graph: f(x) = x + 4 indicates a shift 4 units left Vertical Asymptote: x = -4 No vertical shift Horizontal Asymptote: y = 0

  9. Graph: f(x) = – 3 x + 4 indicates a shift 4 units left Vertical Asymptote: x = -4 –3 indicates a shift 3 units down which becomes the new horizontal asymptote y = -3. 1 x + 4 Horizontal Asymptote: y = 0

  10. Graph: f(x) = + 6 x – 1 indicates a shift 1 unit right Vertical Asymptote: x = 1 +6 indicates a shift 6 units up moving the horizontal asymptote to y = 6 x x – 1 Horizontal Asymptote: y = 1

  11. You try!! 2.

  12. How do we find asymptotes based on an equation only?

  13. Vertical Asymptotes (easy one) • Set the denominator equal to zero and solve for x. • Example: • x-3=0 x=3 • So: 3 is a vertical asymptote.

  14. Horizontal Asymptotes (H.A) • In order to have a horizontal asymptote, the degree of the denominator must be the same, or greater than the degree in the numerator. • Examples: • No H.A because • Has a H.A because 3=3. • Has a H.A because

  15. 3 cases

  16. If the degree of the denominator is GREATER than the numerator. • The Asymptote is y=0 ( the x-axis)

  17. If the degree of the denominator and numerator are the same: • Divide the leading coefficient of the numerator by the leading coefficient of the denominator in order to find the horizontal asymptote. • Example: • Asymptote is 6/3 =2.

  18. If there is a Vertical Shift • The asymptote will be the same number as the vertical shift. • (think about why this is based on the examples we did with graphs) • Example: • Vertical shift is 7, so H.A is at 7.

  19. Homework • http://www.kutasoftware.com/FreeWorksheets/Alg2Worksheets/Graphing%20Simple%20Rational%20Functions.pdf

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