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Section 4.6 : Transformations

6. Use transformations to sketch the graph of the following function.

\[f\left( x \right) = \sqrt {x + 4} - 3\]

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Let’s first identify the “base” function (i.e. the function we are transforming). In this case it looks like we are transforming \(g\left( x \right) = \sqrt x \) .

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The function that have here looks like it can be written as,

\[f\left( x \right) = \sqrt {x + 4} - 3 = g\left( {x + 4} \right) - 3\]

Therefore, we can see that the graph of \(f\left( x \right)\) is simply going to be the graph of \(g\left( x \right)\) shifted left by 4 and down by 3.

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Here is a sketch of both the base function (blue dashed curve) and the function we were asked to graph (red solid curve).