Answer:
- vertical expansion by a factor of 2
- translation right 3 units
- translation up 4 units
Step-by-step explanation:
You want the transformations involved in the absolute value function 2|x-3|+4.
Transformations
The transformations we're usually concerned with include ...
- vertical scaling
- horizontal scaling
- translation right
- translation up
The scale factors can be positive or negative (indicating reflection), greater than 1 (expansion) or less than 1 (compression). The translations can be positive or negative (in the opposite direction).
Application
The original absolute value function |x| has been transformed to ...
a|x -h| +k
where 'a' is the vertical scale factor, and (h, k) represent the translation (right, up).
Comparing to 2|x -3| +4, we see a=2, h=3, k=4.
The function has been vertically expanded by a factor of 2 and translated right 3 units and up 4 units.
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Additional comment
The graph confirms this analysis.
