Question

Give the name of the parent function and describe the transformation represented.

Answer 1

5 units to the left and 2 units downwards

Explanation:$f(x)\text{ = |x + 5| - 2}$

The parent function:

f(x) = |x|

Name of parent function is absolute value function

The transformtion from parent function to the new function:

$\begin{gathered} \text{from f(x) = |x| to f(x) = |x + 5| - 2} \\ \text{For translation:} \\ f(x)\text{ = |x + a| (translation to the left)} \\ f(x)\text{ = |x - a| (translation to the right)} \\ \\ So\text{ f(x) = |x + 5| is a translation of 5 units to the left} \end{gathered}$$\begin{gathered} For\text{ translation: } \\ f(x)\text{ = |x| + a (translation upwards)} \\ f(x)\text{ = |x| }-\text{ a (translation downwards)} \\ \\ So\text{ f(x) = |x| - 2 is a translation downwards} \end{gathered}$

Combining both transformation:

f(x) = |x + 5| - 2 is a translation of 5 units to the left and 2 units downwards