Question

fill in the blank.
the graph of ( g(x) = -log_{4} x ) is the graph of ( f(x) = log_{4} x ) reflected about the ______.

the graph of ( g(x) = -log_{4} x ) is the graph of ( f(x) = log_{4} x ) reflected about the
options:

• y - axis.
• line ( y = x )
• x - axis.

Explanation:

To determine the reflection, recall the rules of function transformations. For a function \( y = f(x) \), the transformation \( y = -f(x) \) reflects the graph over the \( x \)-axis. Here, \( g(x)=-\log_{4}x \) is \( -f(x) \) where \( f(x)=\log_{4}x \), so it's a reflection about the \( x \)-axis. Reflecting over the \( y \)-axis would be \( f(-x) \), and reflecting over \( y = x \) is the inverse function, which is not the case here.

Answer:

x - axis.