Question

Identify the domain of the function shown in the graph.

Answer 1

For this case, we find the equation of the line, for this we look for points where the line passes:

`(x1, y1) = (- 2,0)\\(x2, y2) = (- 10, -4)`

We found the slope:

`m = \frac {y2-y1} {x2-x1} = \frac {-4-0} {- 10 - (- 2)} = \frac {-4} {- 10 + 2} = \frac {- 4} {- 8} = \frac {1} {2}`

Thus, the equation of the line is:

`y = \frac {1} {2} x + b`

We substitute a point to find "b":

`0 = \frac {1} {2} (- 2) + b\\0 = -1 + b\\b = 1`

Finally:

`y = \frac {1} {2} x + 1`

Now, the domain is given by all the values for which the function is defined.

It is observed that "x" can take any value, that is, it is defined for all real numbers.

Answer:

Option A