Checkpoint: Transform Logarithmic Functions with Technology Solution

Describe the transformation of the functions f(x) to g(x). Graph g(x).

$f (x) = \log_{2} x g (x) = - \log_{2} (x - 2) + 4$

g(x) is reflected over the x-axis, shifted right 2 units, and shifted up 4 units from f(x).

Note

To graph, use the shortcut keys for a subscript.

Q: Where does the graph intersect the x-axis?
A: (18, 0)

Q: How is it possible for a logarithmic function to cross the x-axis?
A: Since g(x) is transformed, the x-axis is not an asymptote.