Question

Which graph represents the function? f(x)=(x+2)^2 if x<−1

Answer 1

Answer:

option B

Step-by-step explanation:

To get the graph of piecewise function

We make a table for each function

Plug in end points  and make a table

First function f(x) = (x+2)^2 if x<-1

x <-1 so we pick number for x  less than -1. Also we use -1 but we use open circle at x=-1

x         y = (x+2)^2

-3         (-3+2)^2= 1

-2         (-2+2)^2 = 0

-1           (-1+2)^2 = 1

Now plot the table on graph

second function f(x) = |x| + 1 if -1<=x<=1

Make a table, we use -1, 0  and 1 because we have -1<=x<=1 (-1 and 1 are included)

x        y=|x| +1

-1         |1| + 1 = 2

0        |0|+1 = 1

1          |1|+1= 2

Third function  $y=-\sqrt{x}$  if x>1

We find out y when x=1 and make a open circle at x=1 because we have x>1

x       $y=-\sqrt{x}$

1         $-\sqrt{1}=-1$

4         $-\sqrt{4}=-2$

Plot all the point on the graph

Correct graph is attached below