How do you graph the piecewise function #3x+2 , if x ≠ 1#, #8 , if x = 1#?

Question

How do you graph the piecewise function #3x+2 , if x ≠ 1#, #8      , if x = 1#?

Lincoln Anderson · Accepted Answer

undefined To graph the piecewise function $f(x) = \begin{cases} 3x + 2 & \text{if } x \neq 1 \ 8 & \text{if } x = 1 \end{cases}$:

1. For $x \neq 1$, graph the linear function $f(x) = 3x + 2$ over the domain where $x \neq 1$.
2. At $x = 1$, there is a break in the function. At this point, the function jumps to $y = 8$.

Steps:

1. Plot points on the graph for $x \neq 1$, using the linear function $f(x) = 3x + 2$ to draw a line. 
2. Mark an open circle at $x = 1$ (since $x = 1$ is not included in the function $3x + 2$) and draw a horizontal line at $y = 8$ to represent the value of the function at $x = 1$.

The graph will consist of a line segment representing $3x + 2$ for $x \neq 1$, and at $x = 1$, there will be an open circle with a horizontal line at $y = 8$.

Please note that the open circle indicates that the function is not defined at $x = 1$, and the horizontal line at $y = 8$ represents the value of the function at that point.

Liam Brennan · Answer

Draw the line for #y=3x+2# except at the point on the line where #x=1# draw a hollow circle indicating that this point is not included;
then add a filled circle at #(1,8)#

Your graph should look something like: