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Four transformations of the function f(x) = 2x – 4 are given below. For each transformation, drag the expression that shows the result of that transformation into the box under it.
2x – 4 – 3
2(-3x · x) – 4
-3(2x – 4)
2(x – 3) – 4
(2x – 4)(-3x)
2(-3x) – 4
f(x) – 3
f(x – 3)
f(-3x)
-3f(x)
Let’s match each transformation with the corresponding expression.
1. Vertical Shift Down by 3: This transformation takes the function ( f(x) ) and shifts it down by 3 units.
– Match: ( 2x – 4 – 3 ) (which simplifies to ( 2x – 7 )).
– Explanation: This is simply subtracting 3 from the original function.
2. Horizontal Compression by a factor of 3: This transformation compresses the function horizontally.
– Match: ( 2(-3x) – 4 ).
– Explanation: The ( -3x ) reflects a horizontal compression and the multiplication by 2 scales the function vertically.
3. Vertical Reflection: This transformation reflects the function across the x-axis.
– Match: ( -3(2x – 4) ).
– Explanation: The negative sign indicates a reflection.
4. Horizontal Shift to the Right by 3: This transformation shifts the function to the right by 3 units.
– Match: ( 2(x – 3) – 4 ).
– Explanation: This indicates replacing ( x ) with ( x – 3 ), which shifts the graph to the right.
Here’s a quick summary of the matches:
– ( f(x) – 3 ) corresponds