This week we learned how to solve absolute value equations, and then we learned about linear and quadratic reciprocal functions. You can find that there are some patterns that exist when trying to graph reciprocal functions.
reciprocal: one pair of numbers whose product is 1 when multiplied together
- a positive(+) number reciprocates into a positive number
- a negative(-) number reciprocates into a negative number
- both 1 and -1 reciprocates into the same number(doesn’t change), which are called the invariant points
- when 0 is reciprocated it becomes undefined
- big number reciprocate into smaller numbers
- smaller numbers reciprocate into bigger numbers
asymptote: horizontal, vertical, or slanted line that the lines(hyperbola) approach but never touches
hyperbola: two curve lines that are similar to each other, but have opposite reciprocal function points
1) Graph the first linear line, which in is case would be y=2x + 5
- You know the y intercept is 5 and the rise/run is 2/1
2) Notice the where the line intercepts with the x axis, which is where the vertical asymptote of the reciprocal is located
3) Mark the invariant points which are the 1, -1 values on the y axis
4) Graph the Hyperbolas onto the graph based on the recipricals