Functions evaluations and piece-wise definitions

Question

1. let f(x)=|x-1|

a)evaluate f(-5),f(-2),f(1),f(4),f(7)

b)rewrite f(x) without using absolute value symbols by employing a piecewise definition

c)sketch the graph of f(x) over the domain -5≤ x ≤ 7

 

2. let f(x)=|x-5|+|x+3|

a. evaluate f(-6),f(-3),f(0),f(3),f(5),f(8)

b.rewrite f(x) without using absolute value symbols by employing a piecewise definition

c)sketch the graph of f(x) over the domain -6≤ x ≤ 8

Answer 1

I will show you how to do number 1.

 

a)

 

f(c) means to evaluate f(x) at x=c.  So apply this concept to evaluate the following.

 

 

b)

 

f(x) has a V-shape that opens upward.  This V-shape is composed of two straight lines joined together by a single point.  This point is known as the vertex.  The vertex is (1, 0) due to transformation of y=|x|.  So you now know the piecewise function will have 2 linear functions.  One linear function with negative slope, and another with positive slope.

 

The two linear function are then       y = -x + 1          and          y = x - 1

 

f(x) =  {  -x + 1       for     x ≤ 1

               x + 1       for      x > 1      }

 

 

Do the same for question 2.