\[ f(x)=-\left(\frac{2}{3}\right)^{x} \] Plot five points on the graph of the function, and also draw the asymptote.

Step 1 ：Choose some values for x and then calculate the corresponding values of f(x). Let's choose x = -2, -1, 0, 1, 2.

Step 2 ：For x = -2, calculate f(x) = -\((2/3)^{-2}\) = -\((3/2)^2\) = -2.25

Step 3 ：For x = -1, calculate f(x) = -\((2/3)^{-1}\) = -(3/2) = -1.5

Step 4 ：For x = 0, calculate f(x) = -\((2/3)^0\) = -1

Step 5 ：For x = 1, calculate f(x) = -\((2/3)^1\) = -2/3 ≈ -0.67

Step 6 ：For x = 2, calculate f(x) = -\((2/3)^2\) = -4/9 ≈ -0.44

Step 7 ：The five points are (-2, -2.25), (-1, -1.5), (0, -1), (1, -0.67), and (2, -0.44).

Step 8 ：The function f(x) = -\((2/3)^x\) is an exponential function with a base less than 1 (2/3) and a negative sign in front. This means that the function is decreasing and its graph is a reflection of the graph of the function f(x) = (2/3)^x in the x-axis.

Step 9 ：The asymptote of the function is the x-axis (y = 0) because as x goes to positive infinity, f(x) goes to 0 from below, and as x goes to negative infinity, f(x) goes to 0 from above.

Step 10 ：Substitute the x-values into the function and see if we get the corresponding y-values. For example, if we substitute x = 1 into the function, we get f(1) = -\((2/3)^1\) = -2/3, which is the y-value of the point (1, -0.67). This confirms that the points are correct.

Step 11 ：The asymptote y = 0 also meets the requirements of the problem because it is a horizontal line and the function approaches this line as x goes to positive or negative infinity.