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i really really dont know how to do this question and i need it done for my final

 Jun 18, 2019

Best Answer 

 #1
avatar+8718 
+2

We can graph  y = f(x)   by picking  x  values and plotting points.

 

If   x  =  -6,     y  =  |x + 4| - 1  =  |-6 + 4| - 1  =  |-2| - 1  =  2 - 1  =  1     so    (-6, 1)  is on the graph.

 
If   x  =  -5,     y  =  |x + 4| - 1  =  |-5 + 4| - 1  =  |-1| - 1  =  1 - 1  =  0     so    (-5, 0)  is on the graph.

 

 

If   x  =  -4,     y  =  |x + 4| - 1  =  |-4 + 4| - 1  =  |0| - 1  =  0 - 1  =  -1     so    (-4, -1)  is on the graph. 
If   x  =  -3,     y  =  |x + 4| - 1  =  |-3 + 4| - 1  =  |1| - 1  =  1 - 1  =  0     so    (-3, 0)  is on the graph.

 

 

If   x  =  -2,     y  =  -x2 + 3  =  -(-2)2 + 3  =  -4 + 3  =  -1     so    (-2, -1)  is on the graph. 
If   x  =  -1,     y  =  -x2 + 3  =  -(-1)2 + 3  =  -1 + 3  =  2     so    (-1, 2)  is on the graph.

 

 

If   x  =  0,      y  =  -x2 + 3  =  -( 0 )2 + 3  =  0 + 3  =  3     so    (0, 3)  is on the graph. 
  
As we plot the points, we can see what is happening...

 

First we just graph  f(x)  =  |x + 4| - 1  but we only plot the points that have an  x  value less than  -2

 

 

Second we just graph  f(x)  =  -x2 + 3  but we only plot the points with an x value in the interval [-2, 3)

 

And third we would graph  f(x)  =  x  but only plot the points with an  x value greater than or equal to  3

 

 

So far, these are the points we have:

 

 

Notice that the point  (-2, 1)  is NOT on the graph and the point  (-2, -1)  IS on the graph.

 

Do you understand this so far? Do you see how to finish it? If you're still confused please say so!

 Jun 18, 2019
 #1
avatar+8718 
+2
Best Answer

We can graph  y = f(x)   by picking  x  values and plotting points.

 

If   x  =  -6,     y  =  |x + 4| - 1  =  |-6 + 4| - 1  =  |-2| - 1  =  2 - 1  =  1     so    (-6, 1)  is on the graph.

 
If   x  =  -5,     y  =  |x + 4| - 1  =  |-5 + 4| - 1  =  |-1| - 1  =  1 - 1  =  0     so    (-5, 0)  is on the graph.

 

 

If   x  =  -4,     y  =  |x + 4| - 1  =  |-4 + 4| - 1  =  |0| - 1  =  0 - 1  =  -1     so    (-4, -1)  is on the graph. 
If   x  =  -3,     y  =  |x + 4| - 1  =  |-3 + 4| - 1  =  |1| - 1  =  1 - 1  =  0     so    (-3, 0)  is on the graph.

 

 

If   x  =  -2,     y  =  -x2 + 3  =  -(-2)2 + 3  =  -4 + 3  =  -1     so    (-2, -1)  is on the graph. 
If   x  =  -1,     y  =  -x2 + 3  =  -(-1)2 + 3  =  -1 + 3  =  2     so    (-1, 2)  is on the graph.

 

 

If   x  =  0,      y  =  -x2 + 3  =  -( 0 )2 + 3  =  0 + 3  =  3     so    (0, 3)  is on the graph. 
  
As we plot the points, we can see what is happening...

 

First we just graph  f(x)  =  |x + 4| - 1  but we only plot the points that have an  x  value less than  -2

 

 

Second we just graph  f(x)  =  -x2 + 3  but we only plot the points with an x value in the interval [-2, 3)

 

And third we would graph  f(x)  =  x  but only plot the points with an  x value greater than or equal to  3

 

 

So far, these are the points we have:

 

 

Notice that the point  (-2, 1)  is NOT on the graph and the point  (-2, -1)  IS on the graph.

 

Do you understand this so far? Do you see how to finish it? If you're still confused please say so!

hectictar Jun 18, 2019

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