Question

What is the range of the function f(x) = 1/2 x- 2 when the domain is { 2,4,6}

Answer 1

The range of f(x) is:

`y\in\{-1,0,1\}`

Explanation:

Domain and Range

Given a function y=f(x), the domain of f(x) is the set of values that x can take and the range of f(x) is the set of values that f gets when x is in the domain.

We have the function:

`\displaystyle f(x) = (1)/(2) x-2`

And the domain is

`x\in\{2,4,6\}`

Compute the range by assigning each value of x:

For x=2:

`\displaystyle f(2) = (1)/(2) \cdot 2-2=1-2=-1`

`\displaystyle f(2) = -1`

For x=4:

`\displaystyle f(4) = (1)/(2) \cdot 4-2=2-2=0`

`\displaystyle f(4) = 0`

For x=6:

`\displaystyle f(6) = (1)/(2) \cdot 6-2=3-2=1`

`\displaystyle f(6) = 1`

The range of f(x) is:

`y\in\{-1,0,1\}`