Answer:
[tex]f(x) = \left \{ {{x + 3} \quad \text{if} \ -3 \leq x < -1\atop {5} \quad \text{if} \ -1 \leq x \leq1} \right.[/tex]
Step-by-step explanation:
You can find the first function if you know the general form of a line:
[tex]y = mx + b[/tex]
where [tex]m[/tex] is the slope and [tex]b[/tex] the intercept point with the [tex]y[/tex]-axis.
So in the first case the slope is 1 because the next formula
[tex]m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2-0}{-1+3} = 1[/tex]
And you can find the interception point if extend the line, then in our case is 3.
So the function is:
[tex]f(x) = x + 5[/tex]
In the other case is constant function that's mean that the function has the next form
[tex]f(x) = k[/tex]
Where [tex]k[/tex] is a constant.
So you only have to observe what is the value for each point in the interval, in this occasion is 5.
So the final answer is:
[tex]f(x) = \left \{ {{x + 3} \quad \text{if} \ -3 \leq x < -1\atop {5} \quad \text{if} \ -1 \leq x \leq1} \right.[/tex]
