Write the following absolute value function as a piecewise function. f(x) = |2x-6|

Answer 1

f(x) = |2x-6|

f(x) = 2x-6 if x>3

= 6-2x if x< 3

the combination inequality/equality sign can go with either equation

f(x) = 2x-6 if x>3

= 6-2x if x <3

or just do it separately

f(x) =2x-6 if x>3

=6-2x if x<3

= 0 if x=3

graph the absolute value function. It's a

"V" shape with two straight lines, one upward, one downward sloping,

meeting at a vertex = minimum point of the graph = (3,0)

y is always positive. y is at its minimum when x=3