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Filling in a piecewise graph

Hello, I'm having trouble finding the functions for this piecewise function. I've tried what applying what I've learned based on what function graphs should look like, but I keep getting the answer wrong. The question is asking for me to input an algebraic expression for this piecewise graph. Can someone help me?

Re: Filling in a piecewise graph

Re: Filling in a piecewise graph

???

2 if -3<x<=2

2 if 2<x<6

I'm basing my "answers" off what I did on a previous problem where instead of filling in (Formula, if domain is) it was (Formula, what is the domain in interval notation). Am I supposed to write an equation or fill in a number or am I getting the concept entirely wrong.

Re: Filling in a piecewise graph

Hello, DasRabbit!

The graph is not well-defined.

Quote:

Hello, I'm having trouble finding the functions for this piecewise function.

The first (leftmost) segment seems to connect $\displaystyle \left(\text{-}6,\,\tfrac{3}{2}\right)$ with $\displaystyle (\text{-}3,\,3)$

That line has the equation: $\displaystyle y \:=\:\tfrac{1}{2}x + \tfrac{9}{2}$

Next is the horizontal line: $\displaystyle y = 2$

The last line does not pass through any other lattice points.

But it seems to have a *y*-intercept of 6.

Then its equation would be: $\displaystyle y \:=\:\text{-}\tfrac{5}{2}x + 6$

So I have: .$\displaystyle f(x) \;=\;\begin{Bmatrix}\frac{1}{2}x+\frac{9}{2} && \text{if }\text{-}6\,\le\,x\,\le\,\text{-}3 \\ 2 && \text{if }\text{-}3 \,<\,x\,\le 2\;\; \\ \text{-}\frac{5}{2}x+6 && \text{if }2\,<\,x\,\le\,6 \end{Bmatrix}$