For the following function....

Question

f(x)= -x+1    if -1<= (read this as less than or equal to) x<1

 

f(x)= 2         if x=1

 

f(x)= x^2.    if x>1

 

 

a) find f(0)

 

b) find f(1)

 

c) find f(2)

 

d) determine Domain and Range

 

Answer 1

Evaluate each part using the given domain.  For example, f(2) would be evaluated at the last piece of the function.

 

Since the function covers all x values, the domain is all real numbers greater than or equal to -1.  

 

To find range we need to evaluate the pieces at their end domains to see how the function behaves.

 

For the first piece,

 

f(1) = -1 + 1 = 0

 

The last piece is f(1) = 1

 

Since the graph starts out decreasing and then increasing, the range is (0, ∞).