Graphing an integer function and finding its range for a given...
The function $g$ is defined as follows for the domain given.
\[
g(x)=2 x+2, \quad \text { domain }=\{-4,-2,1,3\}
\]
Write the range of $g$ using set notation. Then graph $g$.

Step 1 ：The function $g$ is defined as follows for the domain given: $g(x)=2 x+2$, with domain $\{-4,-2,1,3\}$.

Step 2 ：We need to find the range of the function. The range of a function is the set of all possible output values (y-values) which we get after substituting all the elements of a domain.

Step 3 ：Substitute each value from the domain into the function and calculate the corresponding output. This will give us the range of the function.

Step 4 ：For $x=-4$, $g(x)=2(-4)+2=-6$

Step 5 ：For $x=-2$, $g(x)=2(-2)+2=-2$

Step 6 ：For $x=1$, $g(x)=2(1)+2=4$

Step 7 ：For $x=3$, $g(x)=2(3)+2=8$

Step 8 ：So, the range of the function $g(x) = 2x + 2$ for the domain $\{-4,-2,1,3\}$ is $\{-6, -2, 4, 8\}$.

Step 9 ：Finally, we can plot the function using these domain and range values. The graph of the function is a set of discrete points corresponding to the domain and range values.

Step 10 ：\(\boxed{\text{The range of the function } g(x) = 2x + 2 \text{ for the domain } \{-4,-2,1,3\} \text{ is } \{-6, -2, 4, 8\}}\)