Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

3. Functions

Intro to Functions & Their Graphs

College Algebra

3. Functions

Intro to Functions & Their Graphs

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1:19 minutes

Problem 67

Textbook Question

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

Identify the ordered pairs in the function ƒ. The function is given as ƒ = {(-1,3), (4,7), (0,6), (2,2)}.

To find ƒ(2), look for the ordered pair where the first element (x-value) is 2. In this case, the pair is (2,2).

The second element of the pair (2,2) is the value of ƒ(2). So, ƒ(2) equals the y-value of this pair.

To find ƒ(-1), search for the ordered pair where the first element is -1. The corresponding pair in the function is (-1,3).

The second element of the pair (-1,3) is the value of ƒ(-1). Thus, ƒ(-1) equals the y-value of this pair.

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Key Concepts

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

Function Definition

A function is a relation that assigns exactly one output for each input from its domain. In this context, the function ƒ is represented as a set of ordered pairs, where the first element is the input (or x-value) and the second element is the output (or y-value). Understanding this definition is crucial for determining the outputs for specific inputs.

Evaluating Functions

Evaluating a function involves substituting a given input value into the function to find the corresponding output. For example, to find ƒ(2), you look for the ordered pair where the first element is 2. This process is essential for solving the problem as it directly leads to the required outputs for the specified inputs.

Ordered Pairs

Ordered pairs are pairs of numbers that represent coordinates in a function, typically written as (x, y). In the function ƒ = {(-1,3),(4,7),(0,6),(2,2)}, each pair indicates that for a given x-value, there is a corresponding y-value. Recognizing and interpreting these pairs is vital for accurately finding the outputs for the inputs provided in the question.