Question

graph this function.
f(x)=\begin{cases}2x + 4& \text{if }-5leq xleq1\\-x + 7& \text{if }1<x<5end{cases}
select points on the graph to plot them. select \point fill\ to change a point from closed to open.

Explanation:

Step1: Find points for $y = 2x + 4$ when $- 5\leq x\leq1$

When $x=-5$, $y=2\times(-5)+4=-10 + 4=-6$. When $x = 1$, $y=2\times1+4=6$.

Step2: Find points for $y=-x + 7$ when $1

When $x = 1$ (right - hand limit), $y=-1 + 7=6$ (open - circle as $x>1$ for this part). When $x = 5$ (left - hand limit), $y=-5 + 7=2$ (open - circle as $x<5$ for this part).

Step3: Plot the points

Plot $(-5,-6)$ (closed - circle), $(1,6)$ (closed - circle for $y = 2x + 4$), $(1,6)$ (open - circle for $y=-x + 7$), and $(5,2)$ (open - circle). Connect the points for each part of the piece - wise function.

Answer:

The graph consists of a line segment $y = 2x+4$ from $(-5,-6)$ (closed - circle) to $(1,6)$ (closed - circle) and a line segment $y=-x + 7$ from $(1,6)$ (open - circle) to $(5,2)$ (open - circle).