Ch. R - Algebra Review

Lial12th EditionTrigonometryISBN: 9780136552161Not the one you use?Change textbook

Lial 12th Edition

Ch. R - Algebra Review

Problem 61

Chapter 1, Problem 61

For each function, find (a) ƒ(2) and (b) ƒ(-1). See Example 7. ƒ = {(-1, 3), (4, 7), (0, 6), (2, 2)}

Verified step by step guidance

Understand that the function ƒ is given as a set of ordered pairs, where the first element in each pair is the input (x-value) and the second element is the output (ƒ(x)).

To find ƒ(2), look for the ordered pair where the first element is 2. Identify the corresponding second element in that pair, which represents ƒ(2).

To find ƒ(-1), look for the ordered pair where the first element is -1. Identify the corresponding second element in that pair, which represents ƒ(-1).

If the input value is not found in the set of ordered pairs, then ƒ at that input is undefined for this function.

Write down the values of ƒ(2) and ƒ(-1) based on the pairs found or state that the value is undefined if the input is not present.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Function as a Set of Ordered Pairs

A function can be represented as a set of ordered pairs where each input (x-value) corresponds to exactly one output (y-value). Understanding this helps in identifying the output value for a given input by locating the pair with the matching first element.

Evaluating a Function at a Given Input

Evaluating a function at a specific input means finding the output value associated with that input. For a function defined by ordered pairs, this involves searching the set for the pair whose first element matches the input and then reading off the second element.

Domain and Range of a Function

The domain is the set of all possible input values for a function, while the range is the set of all possible outputs. Knowing the domain helps determine if a function value can be found for a given input, such as checking if 2 or -1 is in the domain before evaluation.

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Related Practice

Textbook Question

In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it. See Examples 5 and 6. center (√2, √2), radius √2

Textbook Question

Graph each function. See Examples 6–8. g(x) = (x - 4)²

Textbook Question

Add or subtract, as indicated. See Example 4. (3/a - 2) - (1/2 - a)

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Textbook Question

Find each product. See Example 5. (2x + 5)³

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Textbook Question

Evaluate each expression. See Example 5. -|4.5|

Textbook Question

Add or subtract, as indicated. See Example 4. (1/(x + z)) + (1/(x - z))

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