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Section 4.6 : Transformations
6. Use transformations to sketch the graph of the following function.
\[f\left( x \right) = \sqrt {x + 4} - 3\]Show All Steps Hide All Steps
Start SolutionLet’s first identify the “base” function (i.e. the function we are transforming). In this case it looks like we are transforming \(g\left( x \right) = \sqrt x \) .
Show Step 2The 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.
Show Step 3Here is a sketch of both the base function (blue dashed curve) and the function we were asked to graph (red solid curve).
