Identify the sequence of even numbers from the given arithmetic progression.

The given arithmetic progression is $1, 2, 3, 4, \dots$.
The even numbers in this sequence are $2, 4, 6, 8, \dots$.
This is an arithmetic progression with:
First term, $a = 2$
Common difference, $d = 4 - 2 = 2$
Number of terms, $n = 12$

The sum of the first $n$ terms of an arithmetic progression is given by:

Substitute the values: $a=2$, $d=2$, $n=12$.

The sum of the first 12 even numbers is $\boxed{\text{156}}$.

4. The range of a function $g(x) = 2x - 1$ is $\{-3, -1, 3, 0\}$. Draw an arrow showing the mapping with its domain.

The function is $g(x) = 2x - 1$. The range is the set of output values, $g(x)$.
We need to find the input values, $x$, for each value in the range.
Let $y = g(x)$. So, $y = 2x - 1$.
To find $x$, rearrange the equation:
$y + 1 = 2x$
$x = \frac{y+1}{2}$

• For $y = -3$: $x = \frac{-3+1}{2} = \frac{-2}{2} = -1$
• For $y = -1$: $x = \frac{-1+1}{2} = \frac{0}{2} = 0$
• For $y = 3$: $x = \frac{3+1}{2} = \frac{4}{2} = 2$
• For $y = 0$: $x = \frac{0+1}{2} = \frac{1}{2}$

So, the domain of the function is $\{-1, 0, 2, \frac{1}{2}\}$.

Domain: $\{-1, 0, 2, \frac{1}{2}\}$
Range: $\{-3, -1, 3, 0\}$

The mapping is as follows: