Question

question #11 true or false. the function ( f(x)=log _{6}(x + 1)-2 ) has had the following transformations applied: shifted left 1, shifted down 2

Explanation:

Step1: Recall transformation rules

For a function \(y = f(x)\), \(y=f(x + h)\) shifts the graph left by \(h\) units (\(h>0\)), and \(y = f(x)-k\) shifts the graph down by \(k\) units (\(k>0\)).
For \(y=\log_{6}(x + 1)-2\), compared to \(y = \log_{6}(x)\), when we change \(x\) to \(x + 1\) (\(h = 1\)), the graph of \(y=\log_{6}(x)\) is shifted left by \(1\) unit. When we subtract \(2\) from \(\log_{6}(x + 1)\) (\(k=2\)), the graph is shifted down by \(2\) units.

Answer:

True