Consider this piecewise function.

[tex]f(x)=\left\{\begin{array}{ll}3, & x \leq-3 \\ 2 x+1, & -3\ \textless \ x\ \textless \ 4 \\ -2, & x \geq 4\end{array}\right.[/tex]

Plot [tex]f(x)[/tex] on the graph.

Plot f ( x ) = 3 for x ≤ − 3 as a horizontal line at y = 3 with a closed circle at ( − 3 , 3 ) .
Plot f ( x ) = 2 x + 1 for − 3 < x < 4 as a line segment from ( − 3 , − 5 ) to ( 4 , 9 ) with open circles at both endpoints.
Plot f ( x ) = − 2 for x ≥ 4 as a horizontal line at y = − 2 with a closed circle at ( 4 , − 2 ) .
Combine the three parts to form the complete piecewise function on the graph.

Explanation

Understanding the Piecewise Function We are given a piecewise function and asked to plot it on a graph. The function is defined as follows:

$f(x)=\left{\begin{array}{ll} 3, & x \leq-3 \ 2 x+1, & -3

Answered by GinnyAnswer | 2025-07-05