Math Benchmark Part 1

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Math Benchmark Part 1

  1. 1. Asymptotes Bryanna Bonner Benchmark Part 1
  2. 2. What Are Asymptotes? <ul><li>It’s a line that your graph approaches but will never touch. </li></ul><ul><li>We often graph functions that have vertical and/or horizontal asymptotes. </li></ul>
  3. 3. Curves and Asymptotes <ul><li>As the curve gets closer to the asymptotes, the space between the graph and the asymptote begins to decrease. And it goes on infinitely. </li></ul>
  4. 4. Horizontal Asymptotes <ul><li>Horizontal line that your graph approaches. </li></ul><ul><li>Parabolas would be considered a horizontal asymptote. </li></ul>It never crosses the x-axis.
  5. 5. F(x)=2 x Horizontal Asymptotes <ul><li>Domain- (-∞,∞) </li></ul><ul><li>Range- (0,∞) </li></ul><ul><li>Intercepts- y intercept is 1. X intercept is 0 </li></ul><ul><li>Location Of Asymptote- The asymptote is located above the x. </li></ul>
  6. 6. Verti cal Asymptotes <ul><li>Are vertical lines that your graph approaches. </li></ul><ul><li>Vertical Asymptotes happen when factors in the denominator equals zero and do not cancel with factors in the numerator </li></ul>
  7. 7. Y= 1/x Vertical Asymptotes <ul><li>The vertical asymptote is zero. The factor in the denominator cannot cancel the factors in the numerator. </li></ul><ul><li>So therefore it makes this a vertical asymptote. </li></ul>
  8. 8. Y= 1/x Vertical Asymptotes <ul><li>Domain- (-∞,∞) </li></ul><ul><li>Range- (-∞,∞) </li></ul><ul><li>Intercepts- 0 intercepts. </li></ul><ul><li>Location Of Asymptotes- The asymptote is located on both the x and y axis. </li></ul>

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