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Rational Functions

Rational Functions. Unit 1 lesson 7. Warm up. With your pairs partner, complete the activity on your handout. Inverse Proportion Review Problem. More f(x) = 1/x…. Using the Rational functions handout , complete the table of values and graph the function. Answer the questions in the boxes.

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Rational Functions

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  1. Rational Functions Unit 1 lesson 7

  2. Warm up • With your pairs partner, complete the activity on your handout. • Inverse Proportion Review Problem

  3. More f(x) = 1/x… • Using the Rational functions handout, complete the table of values and graph the function. • Answer the questions in the boxes.

  4. Discussion of f(x) = 1/x • Domain • All real numbers except zero. • (-∞,0) U (0, +∞) • Range • All real numbers except zero. • (-∞,0) U (0, +∞)

  5. More… • X-intercept: The point where the graph crosses the x axis …(x, 0) There is no x intercept in the basic graph of this function. • Y-intercept: The point where the graph crosses the y axis…(0, y) There is no y intercept in the basic graph of this function.

  6. How do these things change when we transform the parent graph? • With your pairs partner to complete the rational functions extension handout.

  7. Discussion of Transformations Standard Form: f(x) = a + k x – h • If |a| > 1, the graph is a vertical stretch of the parent graph. • If 0< |a| <1, (aka…fraction) the graph is a vertical shrink of the parent graph. • If a< 0, the graph is a reflection in the x axis of the parent function.

  8. Other transformations… • What does the k do to the graph? k translates (slides) the parent graph vertically…k units • Looking at your Rational Functions handout f(x) = 1/x + 2 • k = 2….so what happened to the parent graph?

  9. What about h? • How does h affect the parent graph? h translates the parent graph h units horizontally! (to the left or right ) ***Be careful here because of the “-” sign. Ex. f(x)= 1_ x - 4 This translates the graph to the right 4 units!!!

  10. f(x) = 1 . X + 4 This translates the graph to the left 4 units !!!

  11. What else? • Notice that the graph of f(x) = 1/x Splits …. Asymptotes are lines on a graph which the graph gets very close to, but never touches. Therefore in the case of y = 1/x, the x and y axes are asymptotes.

  12. f(x) = a + k x-h • Horizontal asymptote: y = k • Vertical asymptote: x = h • Try this one: f(x) = 5 - 2 x + 3 • Identify the asymptotes of the graph. x = -3, y = -2 2. Pick values to substitute for x…choose numbers on each side of the vertical asymptote…plot these points. 3. Graph the two branches that pass through the points and approach the asymptotes.

  13. Let’s try another one… • Graph f(x) = 2 + 1 x – 2 2. Identify the domain and range from the graph…hmm…are these numbers related at all to the asymptotes?...hmmm

  14. Guided Practice • Worksheet for Lesson 7

  15. Cars and growing old… • On pp. 429-432, complete the cars and growing old task. Do problems 1 and 2. • Write down any new vocabulary that you encounter. Be prepared to discuss… **We may need to add more on this or leave it out…I’m not sure at this point…

  16. New vocabulary from the task… • Inverse variation… A function that can be written y = k/x…like y = 1/x….hmmm… • k is the constant of variation.. • So if you have y = 2/x…2 is the constant of variation…

  17. Learning Task • Complete the Rational Functions in NASCAR task…Day 1 only… • Complete the task as time allows…

  18. 3-2-1 • List three things about today’s lesson you understood • List two things about today’s lesson you are ok with • List one thing about today’s lesson that you are still confused about

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