Problem 70 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

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 1: 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.

Step 2: 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.

Step 3: 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 \(g(x)=\sqrt{x+1}\).