You plot the graph of this function the way you plot the graph of any function. Find a sufficient number of points to define the graph in the region of interest, plot those points, and draw a smooth curve through them.
F(-Infinity) ≈ 0
F(-2) = 1/25 = .04
F(-1) = 1/5 = .2
F(0) = 1
F(1) = 5
F(2) = 25
F(3) = 125
The asymptote as x tends toward -Infinity is F(x) = 0. The curve is exponential, which means it increases very rapidly for x > 0 (as you can see from the above numbers).
Log[F(x)] = xLog[5]
Plotted on log-log graph paper, the straight line has a slope of Log[5].
F(-Infinity) ≈ 0
F(-2) = 1/25 = .04
F(-1) = 1/5 = .2
F(0) = 1
F(1) = 5
F(2) = 25
F(3) = 125
The asymptote as x tends toward -Infinity is F(x) = 0. The curve is exponential, which means it increases very rapidly for x > 0 (as you can see from the above numbers).
Log[F(x)] = xLog[5]
Plotted on log-log graph paper, the straight line has a slope of Log[5].