Evaluate the logarithmic equation for three values of x that are greater than -1, three values of x that are between -2 and -1, and at x = -1. Show your work. Use the resulting ordered pairs to plot the graph; submit the graph via the Dropbox. State the equation of the line asymptotic to the graph (if any).
y = ln(x + 2)
To evaluate the logarithmic equation y = ln(x + 2) for different values of x, we will substitute those values into the equation and calculate the corresponding y-values.
Let's start by evaluating the equation for three values of x that are greater than -1:
When x = 0:
y = ln(0 + 2) = ln(2)
When x = 1:
y = ln(1 + 2) = ln(3)
When x = 2:
y = ln(2 + 2) = ln(4)
Now, let's evaluate the equation for three values of x that are between -2 and -1:
When x = -1.5:
y = ln(-1.5 + 2) = ln(0.5)
When x = -1.3:
y = ln(-1.3 + 2) = ln(0.7)
When x = -1.1:
y = ln(-1.1 + 2) = ln(0.9)
Finally, we will evaluate the equation at x = -1:
y = ln(-1 + 2) = ln(1) = 0
Now we have the following ordered pairs:
(0, ln(2))
(1, ln(3))
(2, ln(4))
(-1.5, ln(0.5))
(-1.3, ln(0.7))
(-1.1, ln(0.9))
(-1, 0)
To plot the graph, we will plot these points on a coordinate system. Remember that the natural logarithm function, ln(x), has an asymptote at x = 0, which means the graph approaches but never touches the x-axis as x approaches infinity or negative infinity.
After plotting the points, you can draw the curve passing through the points. The graph will be a smooth, increasing curve from left to right, asymptotic to the y-axis.
Once you've plotted the graph, you can submit it via the Dropbox.
I hope this explanation helps you understand how to evaluate the logarithmic equation, plot the graph, and identify the asymptote. If you have any further questions, feel free to ask!