Question

express the function graphed on the axes below as a piecewise function. answer attempt 1 out of 10 $f(x)=\begin{cases} \text{blank} &\text{for blank}\\text{blank} &\text{for blank}end{cases}$

Explanation:

Step1: Find the equation for the left - hand line

The left - hand line passes through points $(-2,-8)$ and $(0, - 4)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-4+8}{0 + 2}=\frac{4}{2}=2$. Using the point - slope form $y - y_1=m(x - x_1)$ with the point $(0,-4)$, the equation is $y=2x-4$. The left - hand line is for $x < 0$.

Step2: Find the equation for the right - hand line

The right - hand line passes through points $(0, - 2)$ and $(5,6)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{6 + 2}{5-0}=\frac{8}{5}=1.6$. Using the point - slope form $y - y_1=m(x - x_1)$ with the point $(0,-2)$, the equation is $y = 1.6x-2$. The right - hand line is for $x\geq0$.

Answer:

$f(x)=

$$\begin{cases}2x - 4&x<0\\1.6x-2&x\geq0\end{cases}$$

$