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How do I write equations for the piecewise function? For C.

How do I write equations for the piecewise function? For C.-example-1
User Ruslan Kuleshov
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Ok, so

Here we have the following piecewise function.

First, notice that the yellow function is a function which comes from some changes to the function:


y=\sqrt[]{x}

If we modify the previous function to get the yellow one, we obtain that the yellow function will be:


y=-3\sqrt[]{-x-4}-1

Notice that this function will exist if


x\leq-4

Now, let's see the blue function. As you can see, it has the form of an absolute value function.

Now, our blue function is a function which comes from some changes to the function:


y=\lvert x\rvert

If we modify the previous function to get the blue one, we obtain that the blue function will be:


y=\lvert(3)/(2)x+3\lvert-1

Notice that the function exists if:


-4Now and finally, the green function has the form of a translated cubic root.<p>Our green function is a function which comes from some changes to the function:</p>[tex]y=\sqrt[3]{x}

If we modify the previous function to get the green one, we obtain that the green function will be:


y=2\sqrt[3]{x-6}+4

As this is a piecewise function, we could write the solution as:

[tex]f(x)=\begin{cases}-3\sqrt[]{-x-4}-1\text{ if }x\leq-4 \\ y=\lvert\frac{3}{2}x+3\lvert-1\text{ if }4

How do I write equations for the piecewise function? For C.-example-1
User Nimish
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3.1k points