Question

A. f(x) = l-2xl - 3
Domain: {1, 2, 3}
Find the range

Answer 1

Hello there!

We are given the function:

`\displaystyle \large - 3 \\`

To find the range, we know that domain is the set of all x-values and also called 'input' while range is the set of all y-values and also called 'output'.

Basic Function - you add the input, you get the output. You add x-value in a function, you get y-value. You add domain, you get range.

So, we substitute x = 1,2 and 3 in the function.

x = 1

`\displaystyle \large - 3 \\ \displaystyle \large - 2 \\`

Recall that any numbers in absolute value are always positive.

`\displaystyle \large{ f(1) = 2 - 3} \\ \displaystyle \large{ f(1) = - 1} \\`

x = 2

`\displaystyle \large f(2) = \\ \displaystyle \large f(2) = \\ \displaystyle \large{ f(2) = 4 - 3} \\ \displaystyle \large{ f(2) = 1}`

x = 3

`\displaystyle \large - 3 \\ \displaystyle \large - 6 \\ \displaystyle \large{ f(3) = 6 - 3} \\ \displaystyle \large{ f(3) = 3}`

Therefore, Range: {-1,1,3}

Let me know if you have any questions!

Topic: Absolute Value Function / Modulus Function