Fun House Mirror

Algebra Level 2

Given the graph \( y = \ln x \), which of these statements describes the transformations to get the graph of \( y = \ln (4x^2 + 4x + 1) \) for \( x > - \frac{1}{2} \)?

\(\quad \text{(1)}\) Translate to the left by 1 and up by \( \ln 4 \), then scale vertically by 2.

\(\quad \text{(2)}\) Translate to the left by \(\frac{1}{2}\) and up by \( \ln 2 \), then scale vertically by 2.

\(\quad \text{(3)}\) Translate to the left by 1 and up by \( \ln 2 \), then scale vertically by 2.

\(\quad \text{(4)}\) Translate to the left by \( \frac{1}{2} \) and up by \( \ln 4 \), then scale vertically by 2.

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