Question

question 1 of 46
which of the following best describes the graph of the logarithmic function
given below?
$f(x) = \log_{0.45} x$
a. translation
b. reflection
c. decreasing
d. increasing

Explanation:

For a logarithmic function \( F(x)=\log_{a}x \), if the base \( a \) satisfies \( 0 < a < 1 \), the function is decreasing. Here, the base of the logarithmic function \( F(x)=\log_{0.45}x \) is \( 0.45 \), and \( 0 < 0.45 < 1 \). So the function is decreasing. Translation involves shifting the graph (not applicable here as there's no shift), reflection would involve a negative sign transformation (not present here), and increasing is incorrect as the base is between 0 and 1 for a decreasing log function.

Answer:

C. Decreasing