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Chapter 2: Problem 70

Begin by graphing the square root function, \(f(x)=\sqrt{x} .\) Then use transformations of this graph to graph the given function. $$g(x)=\sqrt{x+1}$$

Short Answer

Expert verified
The graph of \(g(x)=\sqrt{x+1}\) is the graph of the basic square root function \(f(x)=\sqrt{x}\) shifted to the left by 1 unit.

Step by step solution

01

Graph the basic square root function

Start by graphing the basic square root function, \(f(x)=\sqrt{x}\). This function starts from the origin (0,0) and then extends towards the positive x direction.
02

Understand the transformation

The transformation applied here to graph \(g(x)\) from \(f(x)\) is \(x \to x+1\), which symbolize a horizontal shift. A positive value in the transformation \(x \to x+1\) represents a shift to the left.
03

Apply the transformation and graph the given function

Now, apply the horizontal shift to the graph of \(f(x)\). This means shifting each point of \(f(x)\) to the left by 1 unit. Doing this will give you the graph of the given function \(g(x)=\sqrt{x+1}\).

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