Describe the transformation of the function from y = log (x) to y = 3 log (x + 1) Dilation: Vertical Stretch by a factor of 3 Translation Up 1 Unit Dilation: Vertical Stretch by a factor of 1 Translation Left 1 Unit Dilation: Vertical Compression by a factor of 3 Translation Right 1 Unit
Question
Describe the transformation of the function from y = log (x) to y = 3 log (x + 1) Dilation: Vertical Stretch by a factor of 3 Translation Up 1 Unit Dilation: Vertical Stretch by a factor of 1 Translation Left 1 Unit Dilation: Vertical Compression by a factor of 3 Translation Right 1 Unit
Solution
The transformation of the function from y = log(x) to y = 3 log(x + 1) involves several steps:
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Translation: The "+1" inside the log function translates the graph 1 unit to the left. This is because the "+1" is subtracted from the x-value, shifting the entire graph to the left.
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Dilation: The "3" outside the log function vertically stretches the graph by a factor of 3. This means that the y-values of the graph are multiplied by 3, making the graph appear taller.
Note: The other transformations mentioned (Translation Up 1 Unit, Dilation: Vertical Stretch by a factor of 1, Dilation: Vertical Compression by a factor of 3, Translation Right 1 Unit) are not applicable to the transformation from y = log(x) to y = 3 log(x + 1).
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