One thing I’ve learned this week is about **reciprocal functions**. We’ve always use that word when we divided fractions. We ‘reciprocate’ the fraction we’re dividing with.

Anyways, let’s recall what a reciprocal is:

- the reciprocal of
*x*is - Basically, the reciprocal of a number is just the numerator and denominator switched.
- Remember that all whole numbers and variables are over one.
*They have a denominator of one, basically.*

What we need to remember about this topic are **asymptotes**, one’s called **vertical asymptote** (x value), one’s **horizontal asymptote **(y value). An asymptote is a line that corresponds to the zeroes of your equation.

So, let’s say we have

We must know that we cannot have a **zero on the denominator**, so we’ll first find out which value of x would result to have a zero denominator.

3x + 6 = 0

3x = -6

x = -2

Like was stated earlier, asymptotes are the zeroes to the function. So basically, since we just found out the **zero** of the denominator, we also found out one of the asymptotes. Remember, the vertical asymptote is a value of x, so our vertical asymptote is** (x=-2)**

Right now, though, we don’t need to bother with the horizontal asymptote. Take note that** if the function’s denominator is 1, our horizontal asymptote will always be zero**. (y=0)

So this is how you graph it:

- put a dashed line on where x= -2 is.
- put a dashed line on where y = 0 is.
- If the slope of your original line (3x + 6) is positive, then you will draw the
**hyperbolas**on**quadrant I and III**, and if it’s negative draw it on**quadrant II and IV.** -
*(https://www.varsitytutors.com/hotmath/hotmath_help/topics/quadrants)* - The hyperbolas must
**never touch**the asymptotes, since they are your non-permissible values. - The graph should look like this.: