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.
- The hyperbolas must never touch the asymptotes, since they are your non-permissible values.
- The graph should look like this.: