Questions: Use transformations on the basic function listed below to write a rule (y=f(x) mathrmt) Absolute value function: (f(x)=x) (x) (f(x)) -2 2 -1 1 0 0 1 1 2 2

Transcript text: Use transformations on the basic function listed below to write a rule $y=f(x) \mathrm{t}$ Absolute value function: $f(x)=|x|$ \begin{tabular}{|c|c|} \hline$x$ & $f(x)$ \\ \hline-2 & 2 \\ \hline-1 & 1 \\ \hline 0 & 0 \\ \hline 1 & 1 \\ \hline 2 & 2 \\ \hline \end{tabular}

Solution

Solution Steps

Step 1: Analyze the first graph

The vertex of the absolute value function is at (0,0). The graph passes through points (1,1) and (-1,1). This is the graph of the basic absolute value function, f(x) = |x|.

Step 2: Analyze the second graph

The vertex of the second graph is at (1, -2). This indicates a horizontal shift to the right by 1 unit and a vertical shift downwards by 2 units. The graph also passes through points (2,-1), (0,-1), (3,0), and (-1,0). The slope of the lines are still 1 and -1.

Step 3: Write the transformed function

Based on the transformations observed, the rule for the transformed function is f(x) = |x - 1| - 2.