Graphing y = the square root of x

My younger son and I had an interesting discussion about square roots last night. Thinking through that discussion overnight, I thought it would be fun to have the boys try to graph y = \sqrt{x}. We’ve not really discussed graphs of functions, but introducing the simple idea of graphing was easy enough.

So, I showed quickly how to graph y = x and asked them to repeat the process for y = \sqrt{x}. Here’s what they had on the board when they said they were done:

 

Two nice questions came out of the previous discussion:

(1) What does y = \sqrt{x} look like “near” x = infinity?

(2) What does y = \sqrt{x} look like “near” x = 1?

We tackled infinity first:

 

Next up was the behavior near x = 1. I love the observation by my older son that y = \sqrt{x} is symmetric because at x = \infty it is parallel to the x-axis and near x = 0 it is parallel to the y-axis.

 

We wrapped up with a quick look at the graph on Wolfram Alpha. I love my younger son’s comments when he sees how flat the graph is for large values of x.

 

I’m glad we went through this project. The various specific examples that we’ve been working through in the last couple of weeks have been a nice introduction to square roots, but this project gave both kids some interesting ways to think about the whole function. It also led to some pretty interesting ideas from them about functions and symmetry. Fun little project.

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