writing absolute value equations as a piecewise function

Question

write the absolute value equation as a piecewise function. f(x) = -9|2x-12| = -63.

Answer 1

A piecewise function is a function that is defined on a sequence interval.

For example is a piecewise function.

The absolute function is

Since  

So,      

      

And     

      

Therefore   

               

And           

               

The piecewise function is

Answer 2

A piecewise function is a function that is defined on a sequence interval.

For example is a piecewise function.

The absolute value equation is - 9|2x - 12| = - 63.

|2x - 12| = 7

The absolute value equation |2x - 12| = 7 can be written as

write the absolute value equation as a piecewise function .

The peicewise function graph is

The absolute value equation |2x - 12| = 7.

|2||x - 6| = 7.

|x - 6| = 7/2 = 3.5.

x - 6 = 3.5 and - (x - 6) = 3.5

x = 9.5 and x = 2.5.

Graph the absolute value equation |x - 6| = 3.5 as follows.

On the number line, we can see that each answer is 3.5 units away from 6.

Write the absolute value equation |2x - 12| = 7 as a piecewise function