Question

graph the function
$f(x)=\

$$\begin{cases}-2x - 2&\\text{for }x\\leq - 1\\3x + 1&\\text{for }x > - 1\\end{cases}$$

$. use the least number of pieces possible.
step 1: draw a function piece. select a basic function and transform the graph by moving any $x$ points that appear. if necessary, click any point to restrict the domain.

Explanation:

Step1: Analyze $y = - 2x - 2$ for $x\leq - 1$

When $x=-1$, $y=-2\times(-1)-2=0$. The slope is $m = - 2$ and the $y$-intercept is $b=-2$. Plot the point $(-1,0)$ and use the slope to draw the line for $x\leq - 1$. Since $x\leq - 1$, the line will have a closed - circle at $x = - 1$.

Step2: Analyze $y = 3x + 1$ for $x>-1$

When $x=-1$, $y=3\times(-1)+1=-2$. The slope is $m = 3$ and the $y$-intercept is $b = 1$. Plot the point $(-1,-2)$ (but with an open - circle since $x>-1$) and use the slope to draw the line for $x>-1$.

Answer:

Graph the line $y=-2x - 2$ with a closed - circle at $(-1,0)$ for $x\leq - 1$ and the line $y = 3x+1$ with an open - circle at $(-1,-2)$ for $x>-1$.