The piecewise defined function f(x) is graphed below. What is the value of f(5)?

Explanation:

Draw a vertical line through 5 on the x axis. This represents the equation x = 5. Notice that we intersect the blue line at (5,-1) which tells us that f(5) = -1. There's a closed point here, meaning that the point is included. This is in contrast to the open hole at (5,3) which is not part of the function. So be careful not to say that f(5) = 3 because that's not the case.

were is the equation

(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