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What is the graph of the piecewise-defined function f(x) ? f(x)= x+2 if x<−3 2x if −3≤x<3 x−2 if x≥3

Sagot :

The graph of the function can be plotted using a normal graph plotting

process, ensuring that the expression for f(x) corresponds to the x-value.

Graph of piecewise function:

  • Please find attached the graph of the given piecewise-defined function

Method used to get the graph of the function

The piecewise function is presented as follows;

[tex]f(x) =\begin{cases}x + 2 & \text{ if } x < -3 \\2\cdot x & \text{ if } -3 \leq x < 3 \\x - 2 & \text{ if } x \geq 3\end{cases}[/tex]

The graph of the above piecewise function can be drawn by using a table

of values based on the given input values and the corresponding

expression for f(x) as follows;

[tex]\begin{tabular}{|c|c|c|c|}\underline{x}&\underline{f(x) = x + 2}& \underline{ f(x) = 2\cdot x}& \underline{f(x) = x - 2}\\-8&-6&&\\-7&-5&&\\-6& -4&&\\-5&-3&&\\-4&-2&&\\-3&&-6&\\-2&&-4&\\-1&&-2&\\0&&0&\\1&&2&\\2&&4&\\3&&&1\\4&&&2\\5&&&3\end{array}\right][/tex]

  • The graph of the given piecewise defined function from which  above table of values was formed using MS Excel is attached.

Learn more about piecewise functions here:

https://brainly.com/question/3628123

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