use the graph of the function (f(x)) shown below in order to determine all values of (a) for which…

Explanation:

Step1: Recall limit - definition

The limit $\lim_{x\rightarrow a}f(x) = 0$ means that as $x$ approaches $a$, the value of the function $f(x)$ approaches $0$. We look at the $x$ - values on the graph where the function approaches $y = 0$.

Step2: Examine the graph

By observing the graph of $y = f(x)$ on the interval $-9\lt x\lt9$, we find the $x$ - values for which the function gets arbitrarily close to $y = 0$.

Answer:

The values of $a$ for which $\lim_{x\rightarrow a}f(x)=0$ on the interval $-9\lt x\lt9$ are the $x$ - values where the graph of $y = f(x)$ approaches the $x$ - axis. From the graph, these values may vary depending on the exact shape of the curve, but typically they are the $x$ - intercepts (where the curve crosses or touches the $x$ - axis) within the given interval. Without the actual graph details, we can't give exact numerical values, but conceptually, they are the $x$ - values for which $f(x)$ approaches $0$ as $x$ gets close to them.