Questions: If f(x)=log(x), what is(are) the transformation(s) that occurs if g (2 log(x)? Shifted to the right by 2 Shifted to the left by 2 Shifted up by 2 Shifted down by 2

If f(x)=log(x), what is(are) the transformation(s) that occurs if g (2 log(x)? Shifted to the right by 2 Shifted to the left by 2 Shifted up by 2 Shifted down by 2
Transcript text: If $f(x)=\log (x)$, what is(are) the transformation(s) that occurs if g ( $2 \log (x) ?$ Shifted to the right by 2 Shifted to the left by 2 Shifted up by 2 Shifted down by 2
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Solution

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Solution Steps

Step 1: Identifying Stretch/Compression and Reflection

The parameter \(a = 2\) determines the vertical stretch/compression and reflection. Vertically stretched by a factor of 2.

Step 2: Identifying Shifts

The parameter \(h = 0\) determines the horizontal shift. No horizontal shift. The parameter \(k = 0\) determines the vertical shift. No vertical shift.

Step 3: Identifying Base Change

The parameter \(b = 10\) affects the growth rate of the function. The base of the logarithm is 10, which is common.

Final Answer:

The function \(g(x) = 2\log_{10}(x + 0) + 0\) is characterized by the following transformations:

  • Vertically stretched by a factor of 2.
  • No horizontal shift.
  • No vertical shift.
  • The base of the logarithm is 10, which is common.
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