Question

For f(x) = 2|x+3| – 5, name the type of function and describe each of the three

transformations from the parent function f(x) = |x|

Answer 1

Type of function: Absolute value function
Transformation 1: Stretch vertically by a factor of 2
Transformation 2: Translate left by 3 units
Transformation 3: Translate down by 5 units

Answer 2

There are three transformation i.e. vertically stretch, downward and towards left.

Explanation:

Given : Parent function
`f(x)=|x|` and transformed function
`f(x)=2|x+3|-5`

To find : Name the type of function and describe each of the three transformations?

Solution :

Parent function
`f(x)=|x|` get transformed into
`f(x)=2|x+3|-5`

The transformations are as follow :

1) The function is multiplied by 2 which means there is a transformation vertically by a stretch factor '2'.

2) The function is subtracted by 5 which means there is a transformation downward by a factor '5'.

3) The function inside x value get added by 3 which means there is a transformation left by a factor '3'.

Therefore, There are three transformation i.e. vertically stretch, downward and towards left.