Question 926129
The logarithmic function, {{{y = log(b,x)}}} , can be shifted {{{k}}} units vertically and {{{h}}} units horizontally with the equation 

{{{y = log(b,(x+h))+k}}} .

Vertical shift

If {{{k> 0}}}, the graph would be shifted {{{k}}} units {{{up}}}.

If {{{k < 0}}}, the graph would be shifted {{{k}}} units {{{down}}}.

Horizontal Shift

If {{{h > 0}}}, the graph would be shifted {{{h}}} units {{{left}}}.

If {{{h <0}}}, the graph would be shifted {{{h}}} units {{{right}}}. 

Whenever the minus sign (-) is in front of the function notation, it indicates a reflection across the x-axis. For example, the graph of {{{(-f(x))}}} is a reflection of the graph of {{{f(x)}}} across the x-axis. 

The graph of 3 -g(x) involves the reflection of the graph of g(x) across the x-axis and the upward shift of the reflected graph 3 units. 



you are given:

a logarithmic function with base {{{b=4}}} that has been translated right {{{h=1}}} and up {{{k=5}}} and reflected over the {{{x}}} axis

{{{y = -log(4,(x+1))+5}}} 


{{{ graph( 600, 600, -10, 10, -10, 10,log(4,x),-log(4,(x+1))+5) }}}