Describing Transformations of Radical Functions

We want to use the given graph to write a rule for $g (x) .$

We can see that the graph of $g$ is a vertical stretch by a factor of $2,$ and a horizontal translation left by $1$ unit. Let's consider how these types of transformations affect the equation of the function.

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	$Vertical shrink, 0 < a < 1 y = a f (x)$

Using the table, we can write the transformations of $f (x) .$ $g (x) = 2 f (x + 1) \Rightarrow g (x) = 2 x + 1$

Describing Transformations of Radical Functions 1.11 - Solution