Algebra II Chapter 02 A BowerPoint Presentation

We want to take the graph of a piecewise function and turn it into something that looks like this…

This function appears to have two pieces – one is pink and one is green. What is the value of x when the graph changes from pink to green?

This function changes from pink to green at

The left piece of this function is pink. It includes everything where

The right piece of this function is green. It includes everything where

Now we can write the “if” parts of the function.

We need to change the ??? in the function with m x + b. Let’s start with the pink piece.

What is the slope ( m ) of the pink piece?

m = 2

We can put that slope into the pink piece. m = 2

What is the y - intercept ( b ) of the pink piece?

b = –5

We can put that y -intercept ( b ) in the pink piece. b = –5

The pink piece of the function is done! Let’s switch to the green piece.

What is the slope ( m ) of the green piece?

m = –1/2

We can put that slope into the green piece. m = –1/2

What is the y - intercept ( b ) of the green piece? We will need to extend the green piece to find it!

What is the y - intercept ( b ) of the green piece? Now we can answer the question !

What is the y - intercept ( b ) of the green piece? b = 3/2 (or 1 ½)

We can put that y -intercept ( b ) in the green piece. b = 3/2 (or 1 ½)

That’s it! We have successfully written the piecewise function for this graph!

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