Question

1. $f(x)=\begin{cases}x + 3, &xleq - 4\\-4, &x > - 4end{cases}$

Explanation:

Step1: Analyze the first - part of the piece - wise function

For $x\leq - 4$, the function is $f(x)=x + 3$. When $x=-4$, $f(-4)=-4 + 3=-1$. This is a linear function with a slope of 1 and a y - intercept of 3. We can plot points for $x\leq - 4$ such as when $x=-4,y=-1$; when $x=-5,y=-2$; when $x=-6,y=-3$ and draw a line with a closed - circle at $x = - 4$ (because $x=-4$ is included in this part of the domain).

Step2: Analyze the second - part of the piece - wise function

For $x>-4$, the function is $f(x)=-4$. This is a horizontal line. We draw a horizontal line at $y = - 4$ with an open - circle at $x=-4$ (because $x=-4$ is not included in this part of the domain).

Answer:

The graph consists of a line $y=x + 3$ for $x\leq - 4$ (with a closed - circle at $(-4,-1)$) and a horizontal line $y=-4$ for $x>-4$ (with an open - circle at $(-4,-4)$).