Questions: Use the table of each function to graph f(x). 1. f(x) = x+1-2 2. f(x) = x-4-2 x, f(x) -3, 0 -2, -1 -1, -2 0, -1 1, 0 x, f(x) 1, 1 2, 0 3, -1 4, -2 5, -1

Transcript text: Use the table of each function to graph $f(x)$. 1. $f(x)=|x+1|-2$ 2. $f(x)=|x-4|-2$ \begin{tabular}{|r|r|} \hline$x$ & $f(x)$ \\ \hline-3 & 0 \\ \hline-2 & -1 \\ \hline-1 & -2 \\ \hline 0 & -1 \\ \hline 1 & 0 \\ \hline \end{tabular} \begin{tabular}{|c|c|} \hline$x$ & $f(x)$ \\ \hline 1 & 1 \\ \hline 2 & 0 \\ \hline 3 & -1 \\ \hline 4 & -2 \\ \hline 5 & -1 \\ \hline \end{tabular}

Solution

Solution Steps

Step 1: Identify the functions

The given functions are:

$ f(x) = |x+1| - 2 $
$ f(x) = |x-4| - 2 $

Step 2: Identify the table values for the first function

The table values for $ f(x) = |x+1| - 2 $ are: \[ \begin{array}{|r|r|} \hline x & f(x) \\ \hline -3 & 0 \\ \hline -2 & -1 \\ \hline -1 & -2 \\ \hline 0 & -1 \\ \hline 1 & 0 \\ \hline \end{array} \]

Step 3: Identify the table values for the second function

The table values for $ f(x) = |x-4| - 2 $ are: \[ \begin{array}{|c|c|} \hline x & f(x) \\ \hline 1 & 1 \\ \hline 2 & 0 \\ \hline 3 & -1 \\ \hline 4 & -2 \\ \hline 5 & -1 \\ \hline \end{array} \]

Final Answer

The functions to be plotted are:

$ f(x) = |x+1| - 2 $
$ f(x) = |x-4| - 2 $

{"axisType": 3, "coordSystem": {"xmin": -5, "xmax": 6, "ymin": -3, "ymax": 2}, "commands": ["y = abs(x + 1) - 2", "y = abs(x - 4) - 2"], "latex_expressions": ["$y = |x+1| - 2$", "$y = |x-4| - 2$"]}

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