# Advanced Geometry : How to graph inverse variation

## Example Questions

### Example Question #1 : How To Graph Inverse Variation

Give the vertical asymptote of the graph of the equation

Explanation:

The vertical asymptote is , where  is found by setting the denominator equal to 0 and solving for :

This is the equation of the vertical asymptote.

### Example Question #2 : How To Graph Inverse Variation

Give the -intercept(s), if any, of the graph of the equation

The graph has no -intercept.

The graph has no -intercept.

Explanation:

Set  in the equation and solve for .

This is impossible, so the equation has no solution. Therefore, the graph has no -intercept.

### Example Question #3 : How To Graph Inverse Variation

Give the -intercept(s), if any, of the graph of the equation

The graph has no -intercept.

Explanation:

Set  in the equation and solve for .

The -intercept is

### Example Question #4 : How To Graph Inverse Variation

Give the horizontal asymptote, if there is one, of the graph of the equation

The graph of the equation has no horizontal asymptote.

Explanation:

To find the horizontal asymptote, we can divide both numerator and denominator in the right expression by :

As  approaches positive or negative infinity,  and  both approach 0. Therefore,  approaches , making the horizontal asymptote the line of the equation  .

### Example Question #5 : How To Graph Inverse Variation

Give the -intercept of the graph of the equation .

The graph has no -intercept.

Explanation:

Set  in the equation:

The -intercept is .

### Example Question #1 : How To Graph Inverse Variation

A triangle is made up of the following points:

What are the points of the inverse triangle?

Explanation:

The inverse of a function has all the same points as the original function, except the x values and y values are reversed. The same rule applies to polygons such as triangles.

### Example Question #1 : Graphing

Electrical power can be generated by wind, and the magnitude of power will depend on the wind speed. A wind speed of  (in ) will generate a power of  . What is the minimum wind speed needed in order to power a device that requires  ?

Explanation:

The simplest way to solve this problem is to plug all of the answer choices into the provided equation, and see which one results in a power of  .

Alternatively, one could set up the equation,

and factor, use the quadratic equation, or graph this on a calculator to find the root.

If we were to factor we would look for factors of c that when added together give us the value in b when we are in the form,

.

In our case . So we need factors of  that when added together give us .

Thus the following factoring would solve this problem.

Then set each binomial equal to zero and solve for v.

Since we can't have a negative power our answer is .

### Example Question #191 : Graphing

Compared to the graph , the graph  has been shifted:

units down.

units up.

units to the right.

units down.

units to the left.

units to the left.

Explanation:

The  inside the argument has the effect of shifting the graph  units to the left. This can be easily seen by graphing both the original and modified functions on a graphing calculator.

### Example Question #1 : How To Graph Inverse Variation

If you look at  and  on the same graph. What is the transformation that took place from ?

units to the left

units to the right

units down

units to the right

units up