Question 377823
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).<br>
Since zero and negative exponents can be tricky, I will do a couple of these for you.
For x = 0:
{{{f(0) = (1/3)^0}}}
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(-2) = (1/3)^(-2)}}}
Since a negative exponent means reciprocal this becomes:
{{{f(-2) = (3/1)^(2)}}}
or
{{{f(-2) = (3)^(2)}}}
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.<br>
By the time you are finished with all the given x values, you will have 7 ordered pairs. Plot all seven points.<br>
Since 1/3 to <i>any</i> power is <i>always</i> 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.<br>
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.