Question

graph the following function on the axes provided.$f(x)= \begin{cases} 4x + 19 & \text{for } x < -5 \\2 & \text{for } x = -5 \\x + 3 & \text{for } x > -5end{cases}$line closed circle open circleclick and drag to make a line. click the line to delete it.click on an endpoint of a line to change it.

Explanation:

Step1: Find endpoint for $x < -5$

Substitute $x=-5$ into $4x+19$:
$4(-5)+19 = -20+19 = -1$
This is an open circle at $(-5, -1)$ since $x < -5$ does not include $x=-5$.

Step2: Graph $4x+19$ for $x < -5$

Choose a second point, e.g., $x=-6$:
$4(-6)+19 = -24+19 = -5$
Draw a line from $(-6, -5)$ to the open circle at $(-5, -1)$, extending left.

Step3: Plot point for $x=-5$

$f(-5)=2$, so plot a closed circle at $(-5, 2)$.

Step4: Find endpoint for $x > -5$

Substitute $x=-5$ into $x+3$:
$-5+3 = -2$
This is an open circle at $(-5, -2)$ since $x > -5$ does not include $x=-5$.

Step5: Graph $x+3$ for $x > -5$

Choose a second point, e.g., $x=0$:
$0+3 = 3$
Draw a line from the open circle at $(-5, -2)$ to $(0, 3)$, extending right.

Answer:

1. A line for $y=4x+19$ (left of $x=-5$) with an open circle at $(-5, -1)$
2. A closed circle at $(-5, 2)$
3. A line for $y=x+3$ (right of $x=-5$) with an open circle at $(-5, -2)$