SOLUTION: Draw the graph of f(x) = (1/5)^(x-1)

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Question 1007694: Draw the graph of f(x) = (1/5)^(x-1)
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
here's the graph.

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.

http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut29_negexp.htm

http://www.purplemath.com/modules/fraction3.htm