Determine the piecewise representation of​ f(x) below:

Question

f(x)= |5x-5|

 

f(x)= equation A  if x >= a

         equation  B  if x< b

whats Equation A=?

 whats equation B=?

              a=?

               b=?

Answer 1

An absolute value can be written as 2 equations, one (equation A) when the stuff INSIDE the ABSVAL is positive and the other (equation B) when the (5x-5) is negative.   The place where this changes is at the x-value that makes the inside expression (5x-5) = 0

 

5x-5 = 0

Add 5 to both sides

 

5x = 5

Divide both sides by 5

 

x = 1

 

 

INSIDE positive:   (5x-5) = 5x-5

INSIDE negative:  -(5x-5) = -5x+5

 

 

Put it all together and we get:

 

 

-5x+5    for x<1

5x-5      for x>=1

 

So Equation A is  f(x) = -5x+5

Equation B is   f(x) = 5x-5

a = 1

b = 1