Question

1. how would the equation $f(x) = \log(x - 2) + 8$ be shifted with respect to the parent function?

\bigcirc right 2 units and up 8 units
\bigcirc left 2 units and up 8 units
\bigcirc right 2 units and down 8 units
\bigcirc left 2 units and down 8 units

Explanation:

Step1: Analyze horizontal shift

For a parent function $g(x) = \log(x)$, replacing $x$ with $x - h$ shifts the graph right by $h$ units. Here, $h=2$, so shift right 2 units.

Step2: Analyze vertical shift

Adding $k$ to the parent function shifts the graph up by $k$ units. Here, $k=8$, so shift up 8 units.

Answer:

right 2 units and up 8 units