# Combining transformations of functions

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Examples

**Describe the Combination of Transformations**

Compared to $y = f\left( x \right)$, describe every step of transformations applied to:

$y = - 2f\left[ {3\left( {x + 4} \right)} \right] + 5$**Write the Equation of a Transformed Function**

Transform the function $f\left( x \right) = \frac{1}{x}$ into the function $g\left( x \right)$ by:- stretching horizontally by a factor of 2 about the y-axis
- stretching vertically by a factor of $\frac{3}{5}$ about the x-axis
- vertical translation of 7 units up
- reflection in the y-axis
- horizontal translation of 4 units to the left
- reflection in the x-axis

Write the function for $g(x)$.

**Use "Coordinate Mapping Formula" to Graph a Transformed Function**

Given the graph of $y = f\left( x \right)$ as shown,