Answer:
We have to graph the piecewise-defined function:
f(x)= |x|-4 , if x < 0
-4 , if x ≥ 0
We know that if x <0 then |x| opens up as: -x.
Hence the function f(x) is defined as:
f(x)= -x-4 ; if x < 0
-4 ; if x ≥ 0.
Hence the graph of function f(x) is a linear graph of the type:
y= -x-4 in the interval (-∞,0)
and the graph of the function f(x) is a straight line passing through
y= -4 in the interval [0,∞).
Also the graph is continuous on whole of the real line as limit of the function exist at x=0 and is equal to the value of the function.
f(0)= -4
Hence, the graph is attached to the answer.
( The rest 3 graphs were given to be discontinuous)
Answer:
Step-by-step explanation:
Start by finding the slope of the given line.
Slope of given line
A perpendicular bisector cuts through the line at its midpoint perpendicularly.
The product of the slopes of two perpendicular lines is -1.
Let the slope of the perpendicular bisector be m.
, where c is the y-intercept.
To find the value of c, we need to substitute a pair of coordinates that lies on the perpendicular bisector into the equation. Since the perpendicular bisector passes through the midpoint of the given line, we can use the midpoint formula to find the coordinates.
Midpoint of given line
= (0, 2)
When x= 0, y= 2,
2= ⅔(0) +c
2= 0 +c
c= 2
Thus, the equation of the perpendicular bisector is .