Math Lesson 15.4.4 - How to Find the Equation of a Reciprocal Graph?

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Welcome to our Math lesson on How to Find the Equation of a Reciprocal Graph?, this is the fourth lesson of our suite of math lessons covering the topic of Reciprocal Graphs, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

How to Find the Equation of a Reciprocal Graph?

Sometimes we have the graph of a reciprocal function given but not the function's formula. We can find it by following the procedure below:

Step 1: Assume the function's formula to be in the form

Step 2: Check whether you are able to determine the equations of asymptotes by sight. This is possible if the units are clearly defined (as in all our examples where the units are shown by the squares). If you can find the asymptotes, then you have found the values of h and k in the above formula.

Step 3: After having identified the position of asymptotes, substitute the coordinates of a known point on the graph to find the coefficient a. If the asymptotes cannot be determined by sight, then solve a system of three equations obtained when you substitute the coordinates of three known points of the graph in the general formula above. It is impossible to solve a system of three equations with the concepts explained so far, but you will learn how to solve them in the upcoming topics of this course when dealing with matrices and determinants.

Example 7

Which function is shown in the graph below?

Solution 7

From the figure, it is clearly visible that x = 3 is a vertical asymptote and y = 2 is a horizontal one. Therefore, we have h = 3 and k = 2. Likewise, we can see that the point with coordinates (4, 3) is a point of the graph. Hence, for x = 4, y = 3, h = 3 and k = 2, we have

Hence, the equation of the hyperbola shown in the graph is

You have reached the end of Math lesson 15.4.4 How to Find the Equation of a Reciprocal Graph?. There are 5 lessons in this physics tutorial covering Reciprocal Graphs, you can access all the lessons from this tutorial below.

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Enjoy the "How to Find the Equation of a Reciprocal Graph?" math lesson? People who liked the "Reciprocal Graphs lesson found the following resources useful:

1. Equation Feedback. Helps other - Leave a rating for this equation (see below)
2. Types of Graphs Math tutorial: Reciprocal Graphs. Read the Reciprocal Graphs math tutorial and build your math knowledge of Types of Graphs
3. Types of Graphs Revision Notes: Reciprocal Graphs. Print the notes so you can revise the key points covered in the math tutorial for Reciprocal Graphs
4. Types of Graphs Practice Questions: Reciprocal Graphs. Test and improve your knowledge of Reciprocal Graphs with example questins and answers
5. Check your calculations for Types of Graphs questions with our excellent Types of Graphs calculators which contain full equations and calculations clearly displayed line by line. See the Types of Graphs Calculators by iCalculator™ below.
6. Continuing learning types of graphs - read our next math tutorial: Exponential Graphs

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