Evaluate the exponential equation for 3 positive values of x, 3 negative values of x, and at x=0. Show all work. Use the resulting ordered pairs to plot the graph; state the equation to the line asymptotic to the graph (if any). y = (1/5)^x
To evaluate the exponential equation y = (1/5)^x, we need to substitute the given values of x into the equation and calculate the corresponding values of y.
Let's choose three positive values for x, such as x = 1, 2, and 3.
For x = 1:
y = (1/5)^1 = 1/5 = 0.2
For x = 2:
y = (1/5)^2 = 1/25 = 0.04
For x = 3:
y = (1/5)^3 = 1/125 = 0.008
Now, let's choose three negative values for x, such as x = -1, -2, and -3.
For x = -1:
y = (1/5)^(-1) = 5
For x = -2:
y = (1/5)^(-2) = 25
For x = -3:
y = (1/5)^(-3) = 125
Finally, let's evaluate the equation at x = 0.
For x = 0:
y = (1/5)^0 = 1
Now, we have the following ordered pairs:
(1, 0.2), (2, 0.04), (3, 0.008) for the positive x values,
(-1, 5), (-2, 25), (-3, 125) for the negative x values, and
(0, 1) for x = 0.
Using these ordered pairs, we can plot the graph on a coordinate plane.
Regarding the line asymptotic to the graph, since the base of the exponential equation is less than 1, the graph of y = (1/5)^x will approach the x-axis (y = 0) as x approaches positive or negative infinity. Therefore, the equation of the line asymptotic to the graph is y = 0.