Answer:
(-1, 7)
Step-by-step explanation:
The given point tells you the value of f(-2) is -1, so ...
-3f(-2) +4 = -3(-1) +4 = 7 . . . . the y-value of the transformed point
The x-value that makes the function argument be -2 is ...
1/2(x -3) = -2
x -3 = -4 . . . . . . multiply by 2
x = -1 . . . . . . . . . add 3
So, the transformed point that corresponds to the given point is ...
(x', y') = (-1, 7)
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If you want to consider the transformations (as the problem suggests), consider this.
-3f(1/2(x -3)) +4
is a vertical expansion by a factor of -3, then translation upward by 4. It is also a horizontal expansion by a factor of 2, then a shift right by 3.
The combinations of these transformations means ...
(x, y) ⇒ (2x+3, -3y+4)
(-2, -1) ⇒ (2(-2) +3, -3(-1) +4) = (-4+3, 3+4) = (-1, 7)
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a·f(b(x-c))+d
is a vertical expansion by 'a', an upward shift of 'd', a horizontal compression by 'b' and a right shift of 'c'. Negative values for 'a' or 'b' represent reflections in the x- or y-axis, respectively.
Here, the compression is by a factor of 1/2, equivalent to expansion by a factor of 1/(1/2) = 2.
