Pablo was graphing a function and noticed that at certain points, the graph reaches invisible lines the graph will never cross. Explain to Pablo what the two types of invisible lines are and how to predict them. You may create your own example to aid in your reasoning. Use complete sentences.

Question

anonymous · Answer

I need some help working it out, Im really terrible with graphs!

hero · Answer

What concepts are you currently studying in class. Try to list as many as you can.

anonymous · Answer

Well, mostly working with polynomials and functions are what not, and asymptotes as well. Oh, and rational expressions too. Does that help?

hero · Answer

The invisible lines are known as asymptotes. The graph can't cross such lines because it would make the rational expression undefined or cause the rational equation to be false.

hero · Answer

For example, consider the graph of the function

$$y = \frac{x}{x - 2}$$

Then x = 2 is an asymptote that the graph will never cross because, if x = 2, then you would have:

$$y = \frac{2}{2 - 2} = \frac{2}{0}$$ But the denominator of a fraction can never equal zero. 

y = 1 is an asymptote the graph will never cross because if y = 1, then:

$$1 = \frac{x}{x - 2}$$
$$x - 2 = x$$
$$x - x = 2$$
$$0 = 2$$ False

hero · Answer

This is what the graph looks like. I included the asymptotes to demonstrate how the graph will never cross them: https://www.desmos.com/calculator/jtdwuvdadf

hero · Answer

To demonstrate you understanding of this, try to keep zooming in to see if the red graph ever touches the blue or green graphs

anonymous · Answer

Thanks ! You've been a big help!

hero · Answer

yw :)