2. (MG 8, Section 5 Purple). For the three exercises below, use a graph and the Horizontal Line Test to determine if each function represents a one-to-one function. Explain your reasoning. (a) f(x) =x² +3x+2 (b) f(x) =x³ – 5x+10 (c) f(x) =x³ +5x+10
2. (MG 8, Section 5 Purple). For the three exercises below, use a graph and the Horizontal Line Test to determine if each function represents a one-to-one function. Explain your reasoning. (a) f(x) =x² +3x+2 (b) f(x) =x³ – 5x+10 (c) f(x) =x³ +5x+10
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.
Question
![**Educational Content: Understanding One-to-One Functions Using the Horizontal Line Test**
In this exercise, we will use the Horizontal Line Test to determine if each function represents a one-to-one function. A function is considered one-to-one if no horizontal line intersects its graph more than once.
**Exercise 2 (MG 8, Section 5 Purple):**
(a) \( f(x) = x^2 + 3x + 2 \)
(b) \( f(x) = x^3 - 5x + 10 \)
(c) \( f(x) = x^3 + 5x + 10 \)
**Instructions:**
1. **Graph the Function:** Plot each function on a graph to visually assess their behavior.
2. **Apply the Horizontal Line Test:** For each graph, imagine or draw horizontal lines across different parts of the graph. If any horizontal line intersects the graph more than once, the function is not one-to-one.
3. **Explain Your Reasoning:** Based on your observations from the graphs, explain why each function is or isn't one-to-one.
**Note:** This exercise helps deepen the understanding of function characteristics and provides a visual approach to analyzing mathematical properties.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe6cad9fc-aa22-494d-997b-d7e31e29d4fe%2F708e4791-333c-497e-88ba-3769bbf4a902%2Fhkqv59n_processed.png&w=3840&q=75)
Transcribed Image Text:**Educational Content: Understanding One-to-One Functions Using the Horizontal Line Test**
In this exercise, we will use the Horizontal Line Test to determine if each function represents a one-to-one function. A function is considered one-to-one if no horizontal line intersects its graph more than once.
**Exercise 2 (MG 8, Section 5 Purple):**
(a) \( f(x) = x^2 + 3x + 2 \)
(b) \( f(x) = x^3 - 5x + 10 \)
(c) \( f(x) = x^3 + 5x + 10 \)
**Instructions:**
1. **Graph the Function:** Plot each function on a graph to visually assess their behavior.
2. **Apply the Horizontal Line Test:** For each graph, imagine or draw horizontal lines across different parts of the graph. If any horizontal line intersects the graph more than once, the function is not one-to-one.
3. **Explain Your Reasoning:** Based on your observations from the graphs, explain why each function is or isn't one-to-one.
**Note:** This exercise helps deepen the understanding of function characteristics and provides a visual approach to analyzing mathematical properties.
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