A student graphed a square root function. What is the equation of the function grap...

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Problem

A student graphed a square root function. What is the equation of the function graphed?

Step-by-step solution

The graph starts at (4,0) and passes through (8,1). The general form of a square root function is $y = a\sqrt{x-h} + k$. From the graph, $(h,k) = (4,0)$. Substituting (8,1) into $y = a\sqrt{x-4}$ gives $1 = a\sqrt{8-4}$, so $1 = a\sqrt{4}$, which means $1 = 2a$, and $a = 1/2$.

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Answer

$y = \frac{1}{2}\sqrt{x-4}$