Question

graph this function.
$f(x)=\

$$\begin{cases}-4x&\\text{if }x\\leq - 1\\4x - 3&\\text{if }x > - 1\\end{cases}$$

$
select points on the graph to plot them. select \point fill\ to change a point from closed to open.

Explanation:

Step1: Analyze $x\leq - 1$ part

For $y = - 4x$ when $x=-1$, $y=-4\times(-1) = 4$. Choose some $x$-values less than - 1, like $x=-2$, then $y=-4\times(-2)=8$. Plot points from this linear - part with a closed - circle at $x = - 1$.

Step2: Analyze $x>-1$ part

For $y = 4x - 3$ when $x=-1$, $y=4\times(-1)-3=-7$. But this part starts at an open - circle at $x=-1$ since the inequality is $x > - 1$. Choose some $x$-values greater than - 1, like $x = 0$, then $y=4\times0-3=-3$; when $x = 1$, $y=4\times1-3 = 1$. Plot points from this linear - part with an open - circle at $x=-1$.

Answer:

Plot the points as described above to graph the piece - wise function. For $y=-4x$ with $x\leq - 1$, plot points such as $(-2,8),(-1,4)$ (closed - circle at $(-1,4)$). For $y = 4x - 3$ with $x>-1$, plot points such as $(0, - 3),(1,1)$ with an open - circle at $(-1,-7)$.