Question

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drag the point to make the graph of
$f(x)=|x - 5|+3$.
try it

Explanation:

Step1: Recall the vertex form of absolute value function

The general form of an absolute value function is \( f(x) = |x - h| + k \), where \((h, k)\) is the vertex of the V - shaped graph.

Step2: Identify h and k from the given function

For the function \( f(x)=|x - 5|+3 \), we can see that \( h = 5 \) and \( k=3 \). So the vertex of the graph should be at the point \((5, 3)\).

Step3: Analyze the current graph

The current vertex of the graph (the purple point) is at \((0, 0)\). To make the graph of \( f(x)=|x - 5|+3 \), we need to move the vertex from \((0, 0)\) to \((5, 3)\). Then, the left - hand side of the V (for \( x<5 \)) will have a slope of - 1 and the right - hand side (for \( x > 5\)) will have a slope of 1, which is consistent with the shape of the absolute value function.

Answer:

To graph \( f(x)=|x - 5|+3 \), move the vertex (the purple point) from \((0, 0)\) to \((5, 3)\). The left part of the V (for \( x<5 \)) will have a slope of - 1 and the right part (for \( x > 5\)) will have a slope of 1, forming the graph of the absolute value function with vertex at \((5, 3)\).