Question

Which graph represents the piecewise - defined function ?

Answer 1

Answer:

The graph is shown below.

Step-by-step explanation:

Given:

Piece wise function

$y=-x-4\textrm{ if }x$

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.