ACT Math : How to graph inverse variation

Study concepts, example questions & explanations for ACT Math

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Example Questions

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?

Possible Answers:

Correct answer:

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 #2 : How To Graph Inverse Variation

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  ?

Possible Answers:

Correct answer:

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 #3 : How To Graph Inverse Variation

Compared to the graph , the graph  has been shifted:

Possible Answers:

 units down.

 units up.

 units to the left.

 units to the right.

 units down.

Correct answer:

 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.  

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