Question

find the value of $f(9)$.
$y = f(x)$
(graph of a piece - wise function with axes labeled x and y, and x - axis from - 10 to 10, y - axis from - 10 to 10)

Explanation:

Step1: Identify right segment equation

First, find the equation for the segment of $y=f(x)$ that includes $x=9$. This is the line passing through $(1,0)$ and, for example, $(9, f(9))$. First calculate the slope:
Slope $m = \frac{0 - (-1)}{1 - 0} = 1$ (using point $(0,-1)$ and $(1,0)$ on this line).
Using point-slope form $y - y_1 = m(x - x_1)$ with $(x_1,y_1)=(1,0)$:
$y - 0 = 1(x - 1)$ so $y = x - 1$.

Step2: Substitute $x=9$ into the equation

Plug $x=9$ into $y = x - 1$:
$y = 9 - 1$

Answer:

$8$