Please help… I am totally lost
Evaluate the exponential equation for three values of x greater than -4, three values of x smaller than -4, and at x = -4. Show your work. Use the resulting ordered pairs to plot the graph. State the equation of the line asymptotic to the graph (if any).
y = 3^(x+4)
Sure! To evaluate the exponential equation y = 3^(x+4) for different values of x, we can substitute those values into the equation and simplify the expression.
Let's start by evaluating for 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 for three values of x smaller than -4:
1. For x = -5:
y = 3^(-5+4) = 3^-1 = 1/3
2. For x = -6:
y = 3^(-6+4) = 3^-2 = 1/9
3. For x = -7:
y = 3^(-7+4) = 3^-3 = 1/27
Lastly, let's evaluate at x = -4:
y = 3^(-4+4) = 3^0 = 1
Now we have the following ordered pairs:
(-3, 3)
(-2, 9)
(-1, 27)
(-5, 1/3)
(-6, 1/9)
(-7, 1/27)
(-4, 1)
To plot the graph, you can use these ordered pairs on a graph with x and y coordinates. Connect the points to see the shape of the exponential graph.
As for the equation of the line asymptotic to the graph, an exponential graph does not have an asymptote in the traditional sense. Exponential graphs grow rapidly as x approaches negative infinity, and they approach y = 0 as x approaches positive infinity. So, there is no specific line asymptotic to the graph of this exponential equation.