Unit 8 Lesson 11 Piecewise Functions

Let’s Review What is our domain? What is our range? What is a function? What is a relation? Why is it important?

Remind me…Is this a function? a. f(x)={(1,6), (2,6), (3,8), (4,9)} b. g(x)={(6,1), (6,2), (8,3), (9,4)} c. d.

Wait…So what is this x and f(x)???

Understanding functions A function is increasing on an interval when the slope is positive ( / ) A function is decreasing on an interval when the slope is negative ( \ ) A function is constant on an interval when there is zero slope (a straight line — )

IMAGES OF WHAT IT LOOKS LIKE FOR A GRAPH TO INCREASE, DECREASE, OR REMAIN CONSTANT

What is a piecewise function? A Function Can be in Pieces We can create functions that behave differently based on the input (x) value. QUESTION: Is the input our Domain (X) or Range (Y)? Here is a function made up of 3 pieces, they can be more or less pieces…

But i’m confused how to name the domain and range…

Let’s look at this function… Here is an example of a piecewise function:   What is h(-1)?   It’s the same as what is h(x)=? What is h(1)? x is ≤ 1, so what is our output when x=1? What is h(4)? x is > 1, so we use h(x) = x, so h(4) = ?

How do we explain it? In the example: when x is less than 2, it gives x2, when x is exactly 2 it gives 6 when x is more than 2 and less than or equal to 6 it gives the line 10-x **Just like INTERVAL NOTATION with inequalities: a solid dot means “including", an open dot means "not including"  

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