Question

graph the following function on the axes provided.
$f(x)=\

$$\begin{cases}3 & \\text{for } \\quad x < 1 \\\\ x + 2 & \\text{for } \\quad x > 5\\end{cases}$$

$
click and drag to make a line. click the line to delete it.
click on an endpoint of a line to change it.

Explanation:

Step1: Graph first piece ($x<1$)

This is a horizontal line $y=3$. It starts at an open circle at $(1, 3)$ (since $x=1$ is not included) and extends left infinitely along $y=3$.

Step2: Graph second piece ($x>5$)

First, find the starting point: when $x=5$, $y=5+2=7$. This is an open circle at $(5, 7)$ (since $x=5$ is not included). The line has a slope of 1, so it extends right and upward, e.g., passing through $(6, 8)$, $(7, 9)$, etc.

Answer:

1. A horizontal line at $y=3$, with an open endpoint at $(1, 3)$, extending to the left across the grid.
2. A line with slope 1, starting at an open endpoint at $(5, 7)$, extending upwards and to the right through points like $(6, 8)$ and $(7, 9)$.