Function: Range Problem

Question

What is the range of the function f ( x ) = xsquared + 4 when the domain is (-2, 5, 7 )??

Answer

Range is the values that a function can take given a domain for its ‘x’ or object value.

In our case,
f ( x ) = xsquared + 4 and domain is (-2, 5, 7 ).

So, we just need to evaluate f(x) at x =-2,5 and 7. Indeed,

f (-2 ) = (-2)squared + 4 = 4 + 4 = 8

f (5 ) = (5)squared + 4 = 25 + 4 = 29

f (7 ) = (7)squared + 4 = 49 + 4 = 53

So the answer is : For the domain (-2, 5, 7 ), the range of our function or equivalently the value of ‘f(x)’ at these ‘x values’ is
(8, 29, 53)

Another way to put it is :

x = (-2, 5, 7 ) yields f(x) = (8, 29, 53)

Where ‘x ‘ is called the ‘object’ while its associated value or
‘f(x)’ is called the ‘range’