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VLD [36.1K]
3 years ago
12

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

Mathematics
1 answer:
gizmo_the_mogwai [7]3 years ago
6 0

Hello there!

We are given the function:

\displaystyle \large{ f(x) =  | - 2x|  - 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.

<u>x</u><u> </u><u>=</u><u> </u><u>1</u>

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

Recall that any numbers in absolute value are always positive.

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

<u>x</u><u> </u><u>=</u><u> </u><u>2</u>

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

<u>x</u><u> </u><u>=</u><u> </u><u>3</u>

\displaystyle \large{ f(3) =  | - 2(3)|  - 3} \\   \displaystyle \large{ f(3) =  | - 6|   - 3} \\   \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

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