Answer: The graph of the given function is shown below,
The given equation is,
[tex]f(x)=|x-2|+3[/tex]
It is a modulus function so graph of the function can be transformed form the standard modulus function g(x)=|x|.
SInce there is subtraction of 2 in the modulus so the graph of g(x) will shift right side by 2 units. Since there is addition of 3 outside the modulus, so the graph will shift upward by 3 units.
The other method is to find the coordinate points.
put x=0
[tex]f(0)=|0-2|+3=5[/tex]
put x=1
[tex]f(1)=|1-2|+3=4[/tex]
put x=2
[tex]f(2)=|2-2|+3=3[/tex]
put x=3
[tex]f(3)=|3-2|+3=4[/tex]
put x=4
[tex]f(4)=|4-2|+3=5[/tex]
So the coordinates are (0,5),(1,4),(2,3),(3,4) and (4,5).
Plot the point and joint them by a straight line. Since it is a modulus function so it is a v-shaped graph.
