Describing Transformations of Radical Functions

We want to describe the transformations of the parent function $f (x) = x$ represented by $g (x) = 2 x - 1 .$ To do so, let's look at the possible transformations. Then we can more clearly identify the ones being applied.

Transformations of $f (x)$
Horizontal Translations	$Translation right h units, h > 0 y = f (x - h)$
Horizontal Translations	$Translation left h units, h > 0 y = f (x + h)$
Vertical Stretch or Shrink	$Vertical stretch, a > 1 y = a f (x)$
Vertical Stretch or Shrink	$Vertical shrink, 0 < a < 1 y = a f (x)$

Now, using the table, let's highlight the transformations. $g (x) = 2 x - 1$ We can describe the transformations as a horizontal translation right $1$ unit and a vertical stretch by a factor of $2 .$ Let's consider the graph of the radical function $f (x) = x .$

Next, we will apply the transformations to the graph of $f (x)$ to obtain the graph of $g (x) .$

Therefore, we have the graph of each function.

Describing Transformations of Radical Functions 1.18 - Solution