### Understanding Functions and Domain/Range ConceptsA graph represents a function if each value of the independent variable, in this case $ x $, corresponds to exactly one value of the dependent variable, $ y $.In the graph below, we observe that there are values of $ x $ that are paired with multiple values of $ y $. This indicates that the graph does not represent a function of $ y $ in terms of $ x $.#### Graph Description- **Graph Type:** It's a wavy line plotted on an $ xy $-coordinate plane.- **Axes:** The horizontal axis is the $ x $-axis, the vertical axis is the $ y $-axis.- **Key Points:** - The line passes through three main points: (6, 46), (6, 20.5), and (6, 2). - These points demonstrate that for $ x = 6 $, there are multiple $ y $-values (46, 20.5, 2), confirming that it's not a function of $ y $ in terms of $ x $.#### Interval Notation and Function AnalysisFor the questions below, use **interval notation**. Use "U" to denote a "union", e.g., "(1,2) U (3,5)" denotes the union of sets $ (1, 2) $ and $ (3, 5) $. Use "oo" to signify infinity, e.g., "(-oo, oo)" means the interval from negative infinity to positive infinity.#### Exercise Questionsa. **Suppose $ f(x) = 2x^2 + 4 $.**i. **What is the domain of $ f $?** (Enter the answer in interval notation)ii. **What is the range of $ f $?** (Enter the answer in interval notation)b. **Suppose $ g(x) = \frac{\sqrt{x - 5}}{x - 8} $.**i. **What is the domain of $ g $?** (Enter the answer in interval notation)ii. **What is the range of $ g $?** (Enter the answer in interval notation)

Answer and explanation is given below

A graph represents a function if each value of the independent variable, in this case a, corresponds to exactly one value of the dependent variable, y. In the below graph we see that there are values of æ that are paired with multiple values of y. We conclude that the graph does not represent the graph of a function of y in terms of a. (6, 46) 35 30 25 20 (6, 20.5) 15 10 (6, 2) 10 For the questions below, enter your answers using interval notation. You can use "U" to represent a "union", e.g. enter "(1,2) U (3,5)" for (1, 2) U (3, 5). You can enter "oo" for oo, e.g. enter "(-00, o0)" for (- 0, 00). a. Suppose f(x) = 2x² + 4. i. What is the domain of f? Preview ii. What is the range of f? Preview b. Suppose g(x) I - 8 i. What is the domain of g? Preview ii. What is the range of g? Preview

A graph represents a function if each value of the independent variable, in this case a, corresponds to exactly one value of the dependent variable, y. In the below graph we see that there are values of æ that are paired with multiple values of y. We conclude that the graph does not represent the graph of a function of y in terms of a. (6, 46) 35 30 25 20 (6, 20.5) 15 10 (6, 2) 10 For the questions below, enter your answers using interval notation. You can use "U" to represent a "union", e.g. enter "(1,2) U (3,5)" for (1, 2) U (3, 5). You can enter "oo" for oo, e.g. enter "(-00, o0)" for (- 0, 00). a. Suppose f(x) = 2x² + 4. i. What is the domain of f? Preview ii. What is the range of f? Preview b. Suppose g(x) I - 8 i. What is the domain of g? Preview ii. What is the range of g? Preview

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

### Understanding Functions and Domain/Range Concepts

A graph represents a function if each value of the independent variable, in this case $ x $, corresponds to exactly one value of the dependent variable, $ y $.

In the graph below, we observe that there are values of $ x $ that are paired with multiple values of $ y $. This indicates that the graph does not represent a function of $ y $ in terms of $ x $.

#### Graph Description

- **Graph Type:** It's a wavy line plotted on an $ xy $-coordinate plane.
- **Axes:** The horizontal axis is the $ x $-axis, the vertical axis is the $ y $-axis.
- **Key Points:**
- The line passes through three main points: (6, 46), (6, 20.5), and (6, 2).
- These points demonstrate that for $ x = 6 $, there are multiple $ y $-values (46, 20.5, 2), confirming that it's not a function of $ y $ in terms of $ x $.

#### Interval Notation and Function Analysis

For the questions below, use **interval notation**. Use "U" to denote a "union", e.g., "(1,2) U (3,5)" denotes the union of sets $ (1, 2) $ and $ (3, 5) $. Use "oo" to signify infinity, e.g., "(-oo, oo)" means the interval from negative infinity to positive infinity.

#### Exercise Questions

a. **Suppose $ f(x) = 2x^2 + 4 $.**

i. **What is the domain of $ f $?**
(Enter the answer in interval notation)

ii. **What is the range of $ f $?**
(Enter the answer in interval notation)

b. **Suppose $ g(x) = \frac{\sqrt{x - 5}}{x - 8} $.**

i. **What is the domain of $ g $?**
(Enter the answer in interval notation)

ii. **What is the range of $ g $?**
(Enter the answer in interval notation)

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