Flashcards
Rational Functions
Cards in this deck (14)
- 1Before drawing / sketching a rational graph, what 4 thing must we work out?1. X and y intercepts
2. Vertical asymptopes
3. Horizontal asymptopes
4. What happens slightly to left and right of each vertical asymptope - 2How to we find the x intercept?Sub 0 into y and rearrange
- 3How do we find the y intercept?Sub 0 into x and rearrange
- 4How to we find where the vertical asymptopes are?Set the denominator equal to 0 and rearrange
(If y=ax+b / cx -d , then cx-d= 0, so x=d/c) - 5How do we find where the horizontal asymptopes are?If y=a+b/x / c+d/x , then y-> a/c
(Divide function through by x, and we can say as x heads towards infinity, 1/x will head towards 0 and any constant will remain the same) - 6How do we find out what happens slightly to the left and right of a vertical asymptope?Lets say a vertical asymptope was at x=5, then we will do the function f(4.99) for the left and f(5.01) for the right. E.g. if the function was y=2x/x+1 , the we would do 2(4.99 or 5.01) / (4.99 or 5.01)+1. Make sure to use fraction button on calculator
- 7A NEGATIVE value for the function of a value slightly do the side of a vertical asymptope tells us what?The graph comes from below, as the y-coordinate is negative
- 8A POSITIVE value for the function of a value slightly do the side of a vertical asymptope tells us what?The graph comes from above, as the y-coordinate is positive
- 9How do we graphically solve an inequality of a rational function like ax+b / cx+d < ex+fSketch the graphs of ax+b / cx+d and ex+f on the same axes, then find the points of intersection and finally solve by inspection.
- 10How do we algebraically solve an inequality of a rational function like ax+b / cx+d < ex+fMultiply both side by the denominator squared and solve (works best for linear functions)
- 11If a ration function tends to the right just to the left of the asymptope, then where is it usually located?Above the horizontal asymptope
- 12If a ration function tends to the left just to the left of the asymptope, then where is it usually located?Below the horizontal asymptope
- 13If a ration function tends to the right just to the right of the asymptope, then where is it usually located?Below the horizontal asymptope
- 14If a ration function tends to the left just to the right of the asymptope, then where is it usually located?Above the horizontal asymptope