Question 1007694
here's the graph.


<img src = "http://theo.x10hosting.com/2015/120301.jpg" alt="$$$" </>


you select values of x and then you use the equation to find values of y.


then you plot them on the graph.


i chose x = -3,-2,-1,0,1,2,3


it was enough to show the general shape of the graph.


two examples of use of the formula are shown below:


when x = -2:


y = (1/5)^(x-1) becomes:


y = 1^(x-1) / (5^(x-1) which becomes:


y = 1 / 5^(-2-1) whicy becomes:


y = 1 / 5^(-3) which becomes:


y = 1 / (1/5^3) which becomes:


y = 1 * 5^3/1 which becomes:


y = 1 * 5^3 which becomes:


y = 1 * 125 which becomes:


y = 125


when x = -2, y = 125 as shown on the graph.


when x = 2 it's a little simpler because you're not dealing with negative exponents.


when x = 2:


y = (1/5)^(x-1) becomes:


y = (1/5)^(2-1) which becomes:


y = (1/5)^1 which becomes:


y = 1/5 which is the same as y = .2 as shown on the graph.


the basic concepts used are:


a^-2 = 1/a^x


this first one means that any value raised to a negative exponent is the same as the reciprocal of that value taised to a positive exponent.


1/(a/b) = 1 * (b/a)


this second one means that, when you divide by a fraction, it's the same thing as multiplying by the reciprocal of the fraction.


some links you might find useful.


<a href = "http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut29_negexp.htm" target = "_blank">http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut29_negexp.htm</a>


<a href = "http://www.purplemath.com/modules/fraction3.htm" target = "_blank">http://www.purplemath.com/modules/fraction3.htm</a>