Function mathematics

Question

Given that f:x ⇒  x²-12,    x≥0 

Find the range of f.

Answer 1

The range is the set of y-values within a domain.  The domain is all x-values greater than or equal to 0.

 

f(0) = 0² - 12

      = -12

 

f(1) = 1² - 12

      =1 - 12

      = -11

 

f(2) = 2² - 12

      = 4 - 12

      = -8

 

f(3) = 3² - 12

      = 9 - 12

      = -3

 

f(4) = 4² - 12

      = 16 - 12

      = 4

 

As you can see, if we keep substituting the domain into the function and evaluating f, f increases from a y-value of -12.

 

The range is  y ≥ -12