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Which function is graphed below?

Which function is graphed below?-example-1
User Slwr
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1 vote

Answer:

Shown below

Explanation:

This is a step function which is a type of function defined by two or more functions. To write the function, we can follow these steps:

STEP 1. A linear function.

This function goes from
-\infty to
2 without including this last value in the domain because at
x=2 we have a hole. By writing the equation:


The \ equation \ of \ the \ line \ with \ slope \ m \\ passing \ through \ the \ point \ (x_(1),y_(1)) \ is:\\ \\ y-y_(1)=m(x-x_(1))

So:


P_(1)(1,0) \\ P_(2)(2,2) \\ \\ y-0=(2-0)/(2-1)(x-1) \\ \\ y=2(x-1) \therefore \boxed{y=2x-2}


f(x)=2x-2, \ \ -\infty<x \leq 2

STEP 2. Constant function.

This function goes from
2 to
5 including both values in the domain because at
x=2 and at
x=5 we have dots.

So:


f(x)=4, \ \ 2 \leq x \leq 5

STEP 3. Linear function.

This is also a linear function but goes from
5 to
+\infty without including
x=5 in the domain because we have a hole here. By writing the equation:

So:


P_(1)(5,6) \\ P_(2)(6,7) \\ \\ y-6=(7-6)/(6-5)(x-5) \\ \\ y=x-5+6 \therefore \boxed{y=x-1}


f(x)=x+1, \ \ 5<x \leq +\infty

Finally, our step function is:


f(x)=\left\{ \begin{array}{c}2x-2,\;-\infty<x\leq2\\4,\;2\leq x\leq5\\x+1,\;5<x\leq+\infty\end{array}\right.

User Pavel Shkleinik
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