Let . Answer the following, justifying each…

MATHEMATICS · Multi-part · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

Let

g(x)=\log_{\tfrac14}x

. Answer the following, justifying each statement: (i) Determine the domain and the range of

g

. (ii) Find the

x

-intercept of the graph of

g

. (iii) Write the equation of every asymptote of the graph of

g

. (iv) State, with reason, whether

g

is an increasing function or a decreasing function on its domain.