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What radical function is represented in the graph? f(x)= (Simplify your answer.)

What radical function is represented in the graph?\newlinef(x)= f(x)= \newline(Simplify your answer.)

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Find limits involving absolute value functionsright chevron icon

Full solution

Q. What radical function is represented in the graph?\newlinef(x)= f(x)= \newline(Simplify your answer.)
  1. Identify Key Points: Identify the key points on the graph where the function intersects the axes or has notable features.
  2. Assume Square Root Function: Assuming the graph passes through the origin (0,0)(0,0), and if it looks like a square root function, then it might be of the form f(x)=axf(x) = a\sqrt{x}.
  3. Check Additional Point: Check if the graph passes through another clear point, for example, 4,y4, y. If y=2y=2, then we can use this point to find 'aa' in f(x)=axf(x) = a\sqrt{x}.
  4. Plug in Coordinates: Plug in the coordinates (4,2)(4, 2) into the equation f(x)=axf(x) = a\sqrt{x} to solve for 'a'. So, 2=a42 = a\sqrt{4}.
  5. Solve for 'a': Since 4=2\sqrt{4} = 2, we have 2=a×22 = a \times 2. Divide both sides by 22 to solve for 'a'. So, a=1a = 1.
  6. Final Function: Now we have the function f(x)=1xf(x) = \frac{1}{\sqrt{x}}, which simplifies to f(x)=xf(x) = \sqrt{x}.

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