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Chapter 3: Problem 24

For each function, find \((a) f(2)\) and \((b) f(-1) .\) See Examples 4 and \(5 .\) $$ f=\\{(-1,-5),(0,5),(2,-5)\\} $$

Short Answer

Expert verified
f(2) = -5, f(-1) = -5

Step by step solution

01

- Identify the function values

The function is defined by the set of ordered pairs \{(-1, -5), (0, 5), (2, -5)\}. Each pair \((x, y)\) represents that when the input is \(x\), the output is \(y\).
02

- Find f(2)

Locate the pair in the set where the first element (input) is 2. The pair \((2, -5)\) shows that when the input is 2, the output (f(2)) is -5. Thus, \(f(2) = -5\).
03

- Find f(-1)

Locate the pair in the set where the first element (input) is -1. The pair \((-1, -5)\) shows that when the input is -1, the output (f(-1)) is -5. Thus, \(f(-1) = -5\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

ordered pairs
In mathematics, an ordered pair is a set of two numbers written in a specific order. An ordered pair looks like this: (x, y).
The first number in the pair is called the 'input' or 'x-coordinate.' The second number is the 'output' or 'y-coordinate.'
Ordered pairs are used to show relationships between two values. For example, in our exercise, you were given the function defined by the set of ordered pairs {(-1, -5), (0, 5), (2, -5)}.
Each of these pairs shows a clear link between the input and output values. Identifying and understanding these pairs is the first step in evaluating functions.
input-output relationship
The input-output relationship in a function shows how each input value (x) is related to a corresponding output value (y).
Think of it as a machine: You put an input into the machine, and it gives you an output. The relationship between these inputs and outputs is what defines the function.
For example, in the ordered pair (2, -5), 2 is the input and -5 is the output.
This means that when you put in 2 into the function, it 'outputs' -5.
Understanding this relationship helps you find the output for any given input within the set.
function notation
Function notation is a way to denote the relationship between inputs and outputs in a function, often written as f(x).
Here, 'f' is the name of the function, and 'x' is the input variable.
When we write f(2), we mean the output value of the function when the input is 2.
In our exercise, given the set of pairs {(-1, -5), (0, 5), (2, -5)}, we found that f(2) = -5 and f(-1) = -5.
This notation simplifies the way we express and work with functions, making it easier to evaluate and understand them.

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