MATH SOLVE

5 months ago

Q:
# Which graph represents the piecewise - defined function ? y = -x -4 if x < -1 2x +1 if x β₯ -1 Any help counts , thanks .

Accepted Solution

A:

Answer:The graph is shown below.Step-by-step explanation:Given:Piece wise function[tex]y=-x-4\textrm{ if }x<-1\\y=2x+1\textrm{ if }x\geq-1[/tex]Let us plot each of the two functions in the given interval.For plotting [tex]y=-x-4[/tex], we find its x and y intercept.For x intercept, put [tex]y=0[/tex]. This gives,[tex]x = -4[/tex]. So, point is (-4,0)For y intercept, put [tex]x = 0[/tex]. This gives, [tex]y=-4[/tex]. So, point is (0,-4)Now, plot these two points and join a straight line. Now [tex]x < -1[/tex]. So we erase the part that is greater the point [tex]x = -1[/tex]. We make a hollow circle at [tex]x=-1[/tex] as [tex]x =-1[/tex] is not in the domain of first function.Similarly, we plot the second line. For x intercept, put [tex]y=0[/tex]. This gives,[tex]x = -0.5[/tex]. So, point is (-0.5,0)For y intercept, put [tex]x = 0[/tex]. This gives, [tex]y=1[/tex]. So, point is (0,1).We erase the line that is less than Β [tex]x =-1[/tex]. We make a solid circle at [tex]x =-1[/tex] as it is in the domain of the second function.Therefore, the graph is as shown below.