### Differentiating and a little bit of manipulating

Well, I guess I'm up. Today in class we worked a bit with some problems using our bank of derivative rules and the chain rule. The questions mostly involved differentiating several functions, and also served to refresh our memories on how the first and second derivatives apply to the parent function. Closer to the end of class today, Mr. K began to tell us how we could take some equations such as the equation of a circle, and manipulate the domain to make it into a function.

For example: if we look at the circular funtion x²+y²=4

On its own, it isnt a function because it fails the vertical line test.

We could break the function the function up into:

f(x)={(4-x²)^½}

{-(4-x²)^½}

Afterwards, we could then manipulate the domains of both of the functions parts. For example:

f(x)={(4-x²)^½; -2 ≤ x ≤ 0}

{-(4-x²)^½; 0 < x ≤ 2}

After the manipulations the function passes the vertical line test and the graph looks like this

Class ended off there, but Mr. K is going to continue this discussion tommorow. See you all tommorow. Scribe for tommorow is Jayson.

For example: if we look at the circular funtion x²+y²=4

On its own, it isnt a function because it fails the vertical line test.

We could break the function the function up into:

f(x)={(4-x²)^½}

{-(4-x²)^½}

Afterwards, we could then manipulate the domains of both of the functions parts. For example:

f(x)={(4-x²)^½; -2 ≤ x ≤ 0}

{-(4-x²)^½; 0 < x ≤ 2}

After the manipulations the function passes the vertical line test and the graph looks like this

Class ended off there, but Mr. K is going to continue this discussion tommorow. See you all tommorow. Scribe for tommorow is Jayson.

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