Question

Please help!!! Express the function graphed on the axes below as a piecewise function

Answer 1

9514 1404 393

Answer:

`f(x)=\left\{\begin{array}{rl}-x-1,&\text{for $-6\le x<2$}}\\-(1)/(2)x-4,&\text{for $2<x<6$}\end{array}\right.`

Explanation:

The upper piece of the graph is defined on the interval -6 ≤ x < 2. It has a slope of -1 and a y-intercept of -1, so its equation is y = -x-1.

The lower piece of the graph is defined on the interval 2 < x < 6. It has a slope of -1/2 and would cross the y-axis at -4 if it were extended. Its equation is ...

y = -1/2x -4

The two pieces together give the function ...

`f(x)=\left\{\begin{array}{rl}-x-1,&\text{for $-6\le x<2$}}\\-(1)/(2)x-4,&\text{for $2<x<6$}\end{array}\right.`