Answer
Asymptote at $y= 0$
Local minimum: (-0.517, -0.131)
See graph below.
Work Step by Step
This question asks for a graph of the function, the asymptotes, and the local maximum and minimum values
The local maximum and minimum values can be calculated with the gray points on the graph in Desmos.
$f(x) = 10^x - 5^x$
The asymptote is at $y= 0$
The local minimum is at (-0.517, -0.131)
See graph below.