SOLUTION: How do I graph f(x)=(1/3)^x substituting the numbers -3,-2,-1,0,1,2,3 for the X values? Thank You.

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Question 377823: How do I graph f(x)=(1/3)^x substituting the numbers -3,-2,-1,0,1,2,3 for the X values? Thank You.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
For each of the x values you have been given, use it to find the value of the function for that x. This will give you a pair of numbers, x and the value of f(x) for that x. These two numbers are the x and y coordinates, respectively, of a point on the graph on f(x).

Since zero and negative exponents can be tricky, I will do a couple of these for you.
For x = 0:
f%280%29+=+%281%2F3%29%5E0
Since any non-zero number to the zero power is one we get:
f(0) = 1
So we have the point (0, 1) when x = 0.
For x = -2:
f%28-2%29+=+%281%2F3%29%5E%28-2%29
Since a negative exponent means reciprocal this becomes:
f%28-2%29+=+%283%2F1%29%5E%282%29
or
f%28-2%29+=+%283%29%5E%282%29
giving us:
f(-2) = 9
So we have the point (-2, 9) when x = -2.
With these two examples you should be able to find the other 5 points.

By the time you are finished with all the given x values, you will have 7 ordered pairs. Plot all seven points.

Since 1/3 to any power is always positive, the graph will always be above the x-axis (where y coordinates are positive). The graph will never touch or cross the x-axis.

Using these points and the fact that the graph never touches or crosses the x-axis we can sketch in the rest of the graph. Draw a smooth curve that goes through the seven point but never touches or crosses the x-axis.