Question

which of the following correctly identifies the transformation of $f(x) = \log_{5}(x + 7)$ from its parent function? (1 point) \
\
\bigcirc horizontal shift left 7 units \
\
\bigcirc vertical shift up 7 units \
\
\bigcirc horizontal shift right 7 units \
\
\bigcirc vertical shift down 7 units

Explanation:

The parent function of \( f(x)=\log_{5}(x + 7) \) is \( g(x)=\log_{5}(x) \). For a function of the form \( y=\log_{b}(x + h) \), when \( h>0 \), the graph is a horizontal shift of the parent function \( y = \log_{b}(x) \) to the left by \( h \) units. Here, \( h = 7>0 \), so \( f(x)=\log_{5}(x + 7) \) is a horizontal shift left 7 units from its parent function.

Answer:

A. horizontal shift left 7 units