what are the features of the function f(x) = log(x + 4) graphed below? answer the function f(x) is function…

Explanation:

Step1: Identify the type of function

The function $f(x)=\log(x + 4)$ is a logarithmic - type function.

Step2: Find the domain

For the logarithm $\log(x + 4)$ to be well - defined, $x+4>0$, so $x>-4$. The domain is $(-4,\infty)$.

Step3: Find the vertical asymptote

As $x\to - 4^{+}$, $\log(x + 4)\to-\infty$. So the vertical asymptote is $x=-4$.

Step4: Determine the range

The range of any logarithmic function of the form $y = \log(u)$ (where $u=x + 4$ here) is $(-\infty,\infty)$.

Step5: Analyze end - behavior on the left

As $x\to - 4^{+}$ (left - hand side approaching the vertical asymptote), $y=\log(x + 4)\to-\infty$.

Step6: Analyze end - behavior on the right

As $x\to\infty$, $y=\log(x + 4)\to\infty$.

Answer:

The function $f(x)$ is a logarithmic function with a vertical asymptote of $x = - 4$. The range of the function is $(-\infty,\infty)$, and it has a domain of $(-4,\infty)$. The end - behavior on the LEFT side is as $x\to - 4^{+},y\to-\infty$, and the end - behavior on the RIGHT side is as $x\to\infty,y\to\infty$.