Describe the transformation of the function from y = log (x) to y = log (x - 2) + 4 Translation Right 4 Units Translation Up 4 Units Translation Up 2 Units Translation Down 4 Units Translation Left 2 Units Translation Right 2 Units
Question
Describe the transformation of the function from y = log (x) to y = log (x - 2) + 4 Translation Right 4 Units Translation Up 4 Units Translation Up 2 Units Translation Down 4 Units Translation Left 2 Units Translation Right 2 Units
Solution
The transformation of the function from y = log(x) to y = log(x - 2) + 4 involves two steps:
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Translation Right 2 Units: The term (x - 2) in the logarithm shifts the graph 2 units to the right. This is because the -2 inside the logarithm function moves the graph in the opposite direction of what you might expect. So, instead of moving to the left (which is what you might expect from subtracting 2), it moves to the right.
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Translation Up 4 Units: The +4 outside the logarithm shifts the graph 4 units upwards. This is because adding a constant outside the function shifts the graph up if the constant is positive (as it is in this case).
So, the transformation from y = log(x) to y = log(x - 2) + 4 involves a translation 2 units to the right and 4 units up.
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