Question

What are the transformations of
g(x) = loga(3-x) + 1
and
t(x) = 2loga 3x

Answer 1

\(\large { g(x) = log_a(3-x) + 1\\ \quad \\\implies
\begin{array}{cccllll}
g(x) = log_a(&-1x+3)& + 1\\
&\uparrow &\uparrow \\
&\textit{horizontal shift}&\textit{vertical shift}\\
&\frac{3}{-1}&+1
\end{array}
\\ \quad \\ \quad \\
\begin{array}{llll}
t(x) = &2log_a &3x\\
&\uparrow &\uparrow \\
\end{array}\\\qquad \textit{vertical stretch} }\)

Answer 2

so for t(x) = 2loga 3x. Its a vertical stretch of 3 or two? a little confused

Answer 3

http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiJsb2coeCkiLCJjb2xvciI6IiMwMDAwMDAifSx7InR5cGUiOjAsImVxIjoiMmxvZyh4KSIsImNvbG9yIjoiI0U2MTAxMCJ9LHsidHlwZSI6MCwiZXEiOiIybG9nKDN4KSIsImNvbG9yIjoiI0U4MTJDRiJ9LHsidHlwZSI6MTAwMH1d <--- they both create a stretch on the graph of the function


this is logarithmic function.. so it goes the the right side
so the factors will expand the value for "y" thus it'll mean a horizontal "expansion"