Use the base to determine points on the graph. Then plot those points and connect them with a smooth curve.
H
Practice makes perfect
To draw the graph of a logarithmic function, we can follow a three-step process.
Identify the base.
Determine points on the graph.
Plot the points and sketch the graph.
Let's do it!
Identify the Base
Looking at the given function, we can see that the base is b= 5.
f(x)=log_5 x
Determine Points on the Graph
Using the base, we can identify three points on the graph of a logarithmic function.
(1,0), ( b,1), and ( 1 b, - 1 )
Since we know that b= 5, we already have that ( b,1) = ( 5,1). Let's now calculate ( 1 b, - 1 ).
Finally, we will plot the three points and connect them with a smooth curve.
We see that the graph will never reach any negative x-value, so the answer can’t be G or J. Moreover, it does not pass through the origin, so F isn't correct either. Therefore, our graph best matches option H.
Extra
Useful Theory
The graph depends on the value of the base b. If b>1, the curve increases. If 0
