Question 1 : Given curve of y = (x^2 - 1)/(x^2 + 1)
- 1. Find domain if curve is deceasing
- 2. Find domain if curve is increasing
- 3. Find domain if curve has extreme points
- 4. Find domain if curve concave downward
- 5. Find domain if curve concave upward
- 6. Find domain if curve has point of inflection
- 7. Find equation of asymptote
Question 2 : Given curve of y = (x^2 - 1)/(x^2 + 1)
- 1. Find domain if y' is negative
- 2. Find domain if y' is positive
- 3. Find domain if y' is zero
- 4. Find domain if y" is negative
- 5. Find domain if y" is positive
- 6. Find domain if y" is zero
Question 3 : Quick sketch y = (x^2 - 1)/(x^2 + 1)
- 1. y-intercept is -1
- 2. Asymptote is y = 1
- 3. If x between -999 and -1, y is between 0 and 1.
- Hence curve is concave downward
- Curve from (-999, 1) to (-1,0)
- 4. If x between -1 and 1, y is negative.
- Hence curve is concave upward
- Curve from (-1,0) to (0, -1) to (1,0)
- 5. If x between 1 and 999, y is between 0 and 1.
- Hence curve is concave downward
- Curve from (1, 0) to (999, 1)
Reference
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