–Reciprocal: The reciprocal is simply: 1/number. To get the reciprocal of a number, we divide 1 by the number.
Example: the reciprocal of 2 is ½ (a half).
-Reciprocal Linear Function: A linear function expressed in the form of 1/f(x), where f(x) is a linear function. Function f(x)’s y-values undergo the transformation of being divided from 1 in order to produce the values of the reciprocal function.
Example: y = 1/x+3.
–Vertical Asymptote (VA): A vertical line that a function may approach, yet never touch. A reciprocal’s vertical asymptotes are located at f(x)’s zeroes. This is due to the fact that at the x-intercepts, they y-values are zero and it is impossible to divide 1 by 0 for the reciprocal function. This means that there are no y-values possible for those specific x-values.
-Horizontal Asymptote (HA): A horizontal line that a function approaches but never touches. An HA is determined by using the ratio of the numerator and denominator’s leading coefficients.
Ex: Graphing a linear function; given f(x) = x+3, graph y = 1/x+
f(x)’s coordinates 1/f(x)’s coordinates
| x | y | x | y |
| -6 | -3 | -6 | 1/-3 |
| -5 | -2 | -5 | 1/-2 |
| -4 | -1 | -4 | 1/-1 |
| -3 | 0 | -3 | N/A |
| -2 | 1 | -2 | 1/1 |
| -1 | 2 | -1 | 1/2 |
| 0 | 3 | 0 | 1/3 |
| 1 | 4 | 1 | 1/4 |
| 2 | 5 | 2 | 1/5 |
| 3 | 6 | 3 | 1/6 |
| 4 | 7 | 4 | 1/7 |
Vertical Asymptote (VA): x=-3
Horizontal Asymptote (HA): y=0 or x-axis