Question

What is the graph to the piecewise defined function g(x) = { x+4, -5<=x<=-1

2-x, -1<=x<=5?

Answer 1

Answer:

third graph, see attached in case the order changes

Step-by-step explanation:

g(x) = { x+4, -5<=x<=-1

            2-x, -1<=x<=5

The graph will change at -1, so we can eliminate the first graph

It changes completely so we can eliminate the second graph

From -5 to -1 the slope is positive 1 so it will increase from left to right

The last graph decreases, so it has a negative slope at -5.  We can eliminate the last graph

That leaves us the third graph

Answer 2

g(x) = x+4, -5《x《-1

At x = -5, g(x) = -1

At x = -1, g(x) = 3

g(x) = 2-x, -1《x《5

At x = -1, g(x) = 3

At x = 5, g(x) = -3