![]() As x goes to zero from the left, the values go to negative infinity. ![]() Our x-values can get infinitely close to zero, and, as they do, the corresponding y-values will get infinitely close to positive or negative infinity, depending which side we approach from. Since this is impossible, there is no output for x=0.īut, what about when x=0.0001? Or when x=-0.0001? It is the point of discontinuity in the function because, if x=0 in the function y= 1/ x, we are dividing by zero. The vertical asymptote is similar to the horizontal asymptote. The horizontal asymptote of y= 1/ x-6 is y=-6. In the basic function, y= 1/ x, the horizontal asymptote is y=0 because the limit as x goes to infinity and negative infinity is 0.Īny vertical shift for the basic function will shift the horizontal asymptote accordingly.įor example, the horizontal asymptote of y= 1/ x+8 is y=8. Horizontal AsymptoteĪ horizontal asymptote is a horizontal line that a function approaches as x gets closer and closer to a specific value (or positive or negative infinity), but that the function never reaches. These three things can help us to graph any reciprocal function. They will also, consequently, have one vertical asymptote, one horizontal asymptote, and one line of symmetry. ![]() Other reciprocal functions are translations, reflections, dilations, or compressions of this basic function. It also has two lines of symmetry at y=x and y=-x. It has a vertical asymptote at x=0 and a horizontal asymptote at y=0. In fact, for any function where m= p/ q, the reciprocal of y=mx+b is y=q/(px+qb). Reciprocal functions are the reciprocal of some linear function.įor example, the basic reciprocal function y= 1/ x is the reciprocal of y=x. For example, the reciprocal of 2 is 1/ 2. Recall that a reciprocal is 1 over a number. When we think of functions, we usually think of linear functions. Why are They Called Reciprocal Functions? In the third quadrant, the function goes to negative infinity as x goes to zero and to zero as x goes to negative infinity. In the first quadrant, the function goes to positive infinity as x goes to zero and to zero as x goes to infinity. For the simplest example of 1/ x, one part is in the first quadrant while the other part is in the third quadrant. The graph of this function has two parts. It can be positive, negative, or even a fraction. What is a Reciprocal Function on a Graph?Ī reciprocal function has the form y= k/ x, where k is some real number other than zero. ![]() What is a Reciprocal Function on a Graph?.Consequently, it is important to review the general rules of graphing as well as the rules for graph transformations before moving on with this topic. Other reciprocal functions are generally some sort of reflection, translation, compression, or dilation of this function. The key to graphing reciprocal functions is to familiarize yourself with the parent function, y= k/ x. Their graphs have a line of symmetry as well as a horizontal and vertical asymptote. Reciprocal functions have the form y= k/ x, where k is any real number. Graphing Reciprocal Functions – Explanation and Examples
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