express the function graphed on the axes below as a piecewise function.
express the function graphed on the axes below as a piecewise function.
Answer
Explanation:
Step1: Find left - hand side line equation
The left - hand side line passes through points (-10, 10) and (-1, 7). The slope $m_1=\frac{y_2 - y_1}{x_2 - x_1}=\frac{7 - 10}{-1+10}=\frac{-3}{9}=-\frac{1}{3}$. Using the point - slope form $y - y_1=m(x - x_1)$ with the point (-10, 10), we get $y-10=-\frac{1}{3}(x + 10)$, which simplifies to $y=-\frac{1}{3}x+\frac{20}{3}$ for $x\leq - 1$.
Step2: Find right - hand side line equation
The right - hand side line passes through points (5, 8) and (9, 0). The slope $m_2=\frac{0 - 8}{9 - 5}=\frac{-8}{4}=-2$. Using the point - slope form $y - y_1=m(x - x_1)$ with the point (5, 8), we get $y - 8=-2(x - 5)$, which simplifies to $y=-2x + 18$ for $x>-1$.
Answer:
[f(x)=\begin{cases}-\frac{1}{3}x+\frac{20}{3},&x\leq - 1\-2x + 18,&x>-1\end{cases}]