Is my answer correct?
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)
Answer=loga y8/7/x4
To evaluate the exponential equation for different values of x, we substitute each value of x into the equation and calculate the corresponding value of y. Let's go through the process step by step:
1. For three values of x greater than -4: Choose three values greater than -4, for example, x = -2, x = 0, and x = 2.
- For x = -2: y = 3(-2 + 4) = 3(2) = 6. So we have the ordered pair (-2, 6).
- For x = 0: y = 3(0 + 4) = 3(4) = 12. So we have the ordered pair (0, 12).
- For x = 2: y = 3(2 + 4) = 3(6) = 18. So we have the ordered pair (2, 18).
2. For three values of x smaller than -4: Choose three values smaller than -4, for example, x = -6, x = -8, and x = -10.
- For x = -6: y = 3(-6 + 4) = 3(-2) = -6. So we have the ordered pair (-6, -6).
- For x = -8: y = 3(-8 + 4) = 3(-4) = -12. So we have the ordered pair (-8, -12).
- For x = -10: y = 3(-10 + 4) = 3(-6) = -18. So we have the ordered pair (-10, -18).
3. At x = -4: Substitute x = -4 into the equation to find y.
- For x = -4: y = 3(-4 + 4) = 3(0) = 0. So we have the ordered pair (-4, 0).
Now, let's plot these points on a graph.
The coordinates of the points we obtained are:
(-2, 6), (0, 12), (2, 18), (-6, -6), (-8, -12), (-10, -18), and (-4, 0).
Plotting these points on a graph, we observe that they all lie on a straight line. The equation of the line is y = 3(x + 4). This graph has a slope of 3 and a y-intercept of 12.
There is no evidence in the original equation to suggest an asymptote for this graph. Therefore, there is no equation of a line asymptotic to the graph in this case.