9514 1404 393
Answer:
[tex]f(x)=\left\{\begin{array}{ccc}3&\text{for}&-5\le x < 0\\1-x&\text{for}&0<x \le 5\end{array}\right.[/tex]
Step-by-step explanation:
The left section is defined at x = -5, but not at x = 0, so the interval for that definition is -5 ≤ x < 0. The function value on that interval is constant: 3.
The right section is defined a x = 5, but not at x = 0, so the interval for that definition is 0 < x ≤ 5. That section is a straight line with a slope of -1 and a y-intercept of 1. The function value on that interval can be written -x+1.
Then the piecewise definition is ...
f(x) = {3, for -5 ≤ x < 0; -x+1, for 0 < x ≤ 5}
