multiple choice 1 point the function h(x)=−ln(x + 1)−2 is a transformation of the function f(x)=lnx. which…

Explanation:

Step1: Analyze reflection

The negative sign in front of $\ln(x + 1)$ in $h(x)=-\ln(x + 1)-2$ reflects the graph of $y = \ln x$ over the $x$-axis. For a function $y = f(x)$, $y=-f(x)$ is a reflection over the $x$-axis.

Step2: Analyze horizontal - translation

For a function $y = f(x)$, the transformation $y = f(x + a)$ ($a>0$) translates the graph $a$ units to the left. In $h(x)=-\ln(x + 1)-2$, compared to $y=\ln x$, the $x$ is replaced with $x + 1$, so the graph is translated 1 unit to the left.

Step3: Analyze vertical - translation

For a function $y = f(x)$, the transformation $y=f(x)-b$ ($b > 0$) translates the graph $b$ units down. In $h(x)=-\ln(x + 1)-2$, compared to $y = \ln x$, there is a subtraction of 2, so the graph is translated 2 units down.

Answer:

The graph of $h(x)$ is the graph of $f(x)$ reflected over the $x$-axis, translated 1 unit to the left and 2 units down.