Question

Complete the first table so that f(x) is a function.

Answer 1

Add the following points to your table.

x  g(x)
-1 -4
-1 -8

By doing this, the input of -1 has two different outputs. They are -4 and -4. Since an input has more than one output, it is not a function.

Answer 2

Answer:

$\left\begin{array}{cc}x&f(x)\\-1&7\\1&-8\\6&-9\end{array}\right$

$\left\begin{array}{cc}x&g(x)\\-1&7\\6&-8\\6&-9\end{array}\right$

Step-by-step explanation:

The given table for $f(x)$ is

$\left\begin{array}{cc}x&f(x)\\-1&--\\--&-8\\6&--\end{array}\right$

For $f(x)$ to be a function, we must complete the table in such a way  that its graph will pass the vertical line test. In order words none of the inputs should repeat.

So we can fill in the blank spaces under x, with any number apart from $-1$ and $6$.

As for the output column, any number at all can go there and $f(x)$ is still a function.

One of the possible solution is;

$\left\begin{array}{cc}x&f(x)\\-1&7\\1&-8\\6&-9\end{array}\right$

The given table for $g(x)$ is

$\left\begin{array}{cc}x&g(x)\\-1&--\\--&-8\\6&--\end{array}\right$

For $g(x)$ not to be a function, we must complete the table in such a way  that its graph will fail the vertical line test. In order words one of the inputs should repeat.

So we can fill in the blank spaces under x, with either $-1$ or $6$.

As for the output column, any number at all can go there and $g(x)$ will still not be a function.

One of the solution is;

$\left\begin{array}{cc}x&g(x)\\-1&7\\6&-8\\6&-9\end{array}\right$