document.write( "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. \n" ); document.write( "

Algebra.Com's Answer #268644 by jsmallt9(3758) $\"\"$ $\"About$

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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).

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

\n" ); document.write( "By the time you are finished with all the given x values, you will have 7 ordered pairs. Plot all seven points.

\n" ); document.write( "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.

\n" ); document.write( "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. \n" ); document.write( "

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