### All ACT Math Resources

## 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:**

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:**

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 down.

units to the right.

units to the left.

**Correct answer:**

units to the left.

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.