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Chapter 2: Problem 67

Begin by graphing the square root function, \(f(x)=\sqrt{x} .\) Then use transformations of this graph to graph the given function. $$g(x)=\sqrt{x}+2$$

Short Answer

Expert verified
The graph of \(g(x)=\sqrt{x} + 2\) is the same as the graph of \(f(x)=\sqrt{x}\), but shifted 2 units upwards.

Step by step solution

01

Graph the basic square root function

Begin by graphing the square root function \(f(x)=\sqrt{x}\). The graph starts from the origin (0,0) and extends towards positive x, looking like the half part of a parabola lying on its side.
02

Understand the transformation

Next, analyze the transformation required to obtain the function \(g(x)\) from \(f(x)\). Here, \(g(x)= f(x) + 2\), which means that every point on the graph of \(f(x)\) is shifted up by 2 units to result in the graph of \(g(x)\). This transformation is a simple vertical shift, and it does not change the shape of the graph.
03

Apply the transformation to the graph

Finally, apply the vertical shift to the graph of the square root function. This means shifting every point of the original graph upwards by 2 units. No points are left out, and because the shape of the graph does not change, it still looks like a half parabola, just translated upwards.

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