Question

Which graph represents the piecewise - defined function ?

y = -x -4 if x < -1
2x +1 if x ≥ -1


Any help counts , thanks .

Answer 1

top left

Explanation:

took the test and got it correct

Answer 2

The graph is shown below.

Explanation:

Given:

Piece wise function

`y=-x-4\textrm{ if }x<-1\\y=2x+1\textrm{ if }x\geq-1`

Let us plot each of the two functions in the given interval.

For plotting
`y=-x-4`, we find its x and y intercept.

For x intercept, put
`y=0`. This gives,
`x = -4`. So, point is (-4,0)

For y intercept, put
`x = 0`. This gives,
`y=-4`. So, point is (0,-4)

Now, plot these two points and join a straight line. Now
`x < -1`. So we erase the part that is greater the point
`x = -1`. We make a hollow circle at
`x=-1` as
`x =-1` is not in the domain of first function.

Similarly, we plot the second line.

For x intercept, put
`y=0`. This gives,
`x = -0.5`. So, point is (-0.5,0)

For y intercept, put
`x = 0`. This gives,
`y=1`. So, point is (0,1).

We erase the line that is less than
`x =-1`. We make a solid circle at
`x =-1` as it is in the domain of the second function.

Therefore, the graph is as shown below.