Answer:
(1, 6)
Explanation:
You want the point on the graph of y = f(-3x) +3 that corresponds to the point (-3, 3) on the graph of y = f(x).
Transformation
The transformation y = f(-3x) +3 has three parts:
- horizontal compression by a factor of 3 (x ⇒ 3x)
- reflection over the y-axis (x ⇒ -x)
- vertical translation up 3 units (f(x) ⇒ f(x)+3)
When we perform these transformation on the point (-3, 3), we see that ...
- horizontal compression: (-3, 3) ⇒ (-1, 3)
- reflection over the y-axis: (-1, 3) ⇒ (1, 3)
- vertical translation up 3 units: (1, 3) ⇒ (1, 6)
The point (-3, 3) on y = f(x) corresponds to the point (1, 6) on the y = f(-3x)+3.
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Additional comment
The mapping of points from y = f(x) to y = f(-3x)+3 is ...
(x, y) ⇒ (-x/3, y+3)
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