Answer:
C f(x)=log(x+2)
Explanation:
To graph the function f(x) = log(x + 2), you can follow these steps:
Determine the domain: Since we have a logarithm function, the domain is the set of values that make the argument inside the logarithm positive. In this case, x + 2 > 0, so x > -2.
Determine any vertical asymptotes: Vertical asymptotes occur when the argument of the logarithm approaches zero or negative infinity. In this case, there is a vertical asymptote at x = -2 because the logarithm is undefined for x = -2.
Find the x-intercept: To find the x-intercept, set f(x) = 0 and solve for x:
0 = log(x + 2)
This equation implies that the argument of the logarithm must be equal to 1 (since log(1) = 0):
x + 2 = 1
x = -1
So the x-intercept is (-1, 0).
Choose additional points: Select some values of x within the domain and evaluate f(x) to get corresponding y-values. For example, you can choose x = -1, 0, 1, and 2.
When x = -1: f(-1) = log((-1) + 2) = log(1) = 0
When x = 0: f(0) = log(0 + 2) = log(2)
When x = 1: f(1) = log(1 + 2) = log(3)
When x = 2: f(2) = log(2 + 2) = log(4)
Plot the points: Plot the x-intercept at (-1, 0) and the additional points you've chosen.
Draw the graph: Connect the points with a smooth curve, keeping in mind the behavior around the vertical asymptote at x = -2. The graph should approach the asymptote but not cross it.
The resulting graph should be a logarithmic curve that approaches the vertical asymptote x = -2 and passes through the x-intercept (-1, 0).
Hope this helps!