Algebra - Transformations

Section 4.6 : Transformations

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

\[f\left( x \right) = \left| {x - 7} \right| + 2\]

Show All Steps Hide All Steps

Start Solution

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

Show Step 2

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

\[f\left( x \right) = \left| {x - 7} \right| + 2 = g\left( {x - 7} \right) + 2\]

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 right by 7 and up by 2.

Show Step 3

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

$The graphs of the base function $g\left( x \right) = \left| x \right|$, the blue dashed curve, and $f\left( x \right) = \left| {x - 7} \right| + 2$, the red solid curve. Both are “V” shaped graphs of exactly the same shape, but the point of the dashed “V” is at the origin while the point of the solid “V” has been shifted 7 units to the right and 2 units up to $\left( {7,2} \right)$.$