Question

Write an equation and graph it to show that it is either a function or not. Provide a picture of your graph

Answer 1

So this is more of an open-ended question. You get to pick a type of function, graph it, and then show if it is a function or not.

The first step is to pick one of these functions. I have them in order from least complicated to most intricate, but you can chose any of these:

Linear:

$y = x$

Quadradic:

$y = {x}^{2}$

Logarithmic:

$y = log_{2}(x)$

Circular:

${x}^{2} + {y}^{2} = 4$

Rational:

$y = \frac{1}{x}$

There are plenty of other types of functions that you can use additionally. Moving on though,

The second step is to show if it is actually a function or not. The easiest way to do this, especially since we are using graphs, is to conduct the verticle line test.

Draw a straight line from top to botom on the graph, then ask yourself "Does it pass through the function more than once?" If it does, then it is not a function, otherwise, you can safely say that the graph is a function. You are going to want to do this more than once.

I included a picture of the graph of the circular equation, and the verticle line tests for it. In the picture, you can clearly see that all of the verticle lines touch the graph more than once.

If you have any other questions, let me know.