Step 1 :The function $h$ is defined as follows for the domain given: $h(x)=2 x-1$, with domain $\{-3,-1,2,4\}$.
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 the domain into the function.
Step 3 :Substitute each value from the domain set $\{-3,-1,2,4\}$ into the function $h(x) = 2x - 1$ and find the corresponding output values.
Step 4 :The output values are $\{-7, -3, 3, 7\}$.
Step 5 :These output values constitute the range of the function.
Step 6 :Plot the function using these domain and range values.
Step 7 :\(\boxed{\text{The range of the function } h(x) = 2x - 1 \text{ for the domain } \{-3,-1,2,4\} \text{ is } \{-7, -3, 3, 7\}.}\)
Step 8 :The graph of the function is a set of discrete points corresponding to these domain and range values.