Evaluate the exponential equation for three values of x greater than -4, three values of x smaller than -4, and at x = -4. Use the resulting ordered pairs to plot the graph. State the equation of the line asymptotic.
y = 3^(x + 4)
To evaluate the given exponential equation for different values of x, we can substitute the given values of x into the equation and calculate the corresponding values of y.
Let's start with three values of x greater than -4:
1. For x = -3:
y = 3^(-3+4) = 3^1 = 3
2. For x = -2:
y = 3^(-2+4) = 3^2 = 9
3. For x = -1:
y = 3^(-1+4) = 3^3 = 27
Now let's evaluate three values of x smaller than -4:
1. For x = -6:
y = 3^(-6+4) = 3^(-2) = 1/9
2. For x = -7:
y = 3^(-7+4) = 3^(-3) = 1/27
3. For x = -8:
y = 3^(-8+4) = 3^(-4) = 1/81
Finally, let's evaluate the equation at x = -4:
y = 3^(-4+4) = 3^0 = 1
Now we have the following ordered pairs:
(-3, 3), (-2, 9), (-1, 27), (-6, 1/9), (-7, 1/27), (-8, 1/81), (-4, 1)
To plot the graph, we can plot these points on a coordinate plane using the x and y values of each ordered pair.
Regarding the equation of the line asymptotic, since the base of the exponential function is 3, the graph will approach but never reach the x-axis (y = 0) as x approaches negative infinity. Therefore, the equation of the line asymptotic for this exponential equation is y = 0.