Which graph represents the function?
g(x) = {x if x < 2
{-3 if x >= 2

Step-by-step explanation:We have to graph the function g(x) which is given as:

g(x)=  x when x<2

and -3 when x ≥2.

Clearly after looking at the function we see that the function is not continuous since we find the continuity at x=2 as follows.

Left hand limitat 2:

g(2-h)=lim h→0 2-h

       =2-0=2

Also right hand limit at x=2 is:

g(2+h)=lim h→0 (2+h)

         = 2+0=2

Also g(2)= -3.

As:

Left hand limit= Right hand limit but is not equal to function's value at that point.

Hence, the function is discontinuous at x=2.

so for x<2 we will get a graph of a line y=x.

and for x≥2 we will get a straight line y=-3 parallel to the domain.

90% rotation

step-by-step explanation:

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3