The graph of f(x) = -4(0.45) is given below (click on graph to enlarge): Let g(x) be the reflection of f(x) across the x-axis. Which of the following graphs represents the graph of g(x)? B◊◊ A. 63 B.
The graph of f(x) = -4(0.45) is given below (click on graph to enlarge): Let g(x) be the reflection of f(x) across the x-axis. Which of the following graphs represents the graph of g(x)? B◊◊ A. 63 B.
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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Transcribed Image Text:The graph of \( f(x) = -4(0.45)^x \) is displayed above. The graph features a curve that starts from negative infinity on the left and gradually approaches zero from below as \( x \) increases.
Next, consider the function \( g(x) \), which is the reflection of \( f(x) \) across the x-axis. This means that all y-values of \( f(x) \) will be inverted, turning them from negative to positive.
Below are four graphs labeled A, B, C, and D. They represent potential reflections of \( f(x) \):
- **Graph A**: Shows a curve starting from positive infinity, decreasing towards zero as \( x \) increases.
- **Graph B**: Displays an upward-curving graph starting from positive infinity, decreasing towards zero on the right side.
- **Graph C**: Presents a similar curve to Graph A but appears as if it could be misaligned.
- **Graph D**: Depicts a different orientation entirely, starting from positive and moving towards negative with increasing \( x \).
The correct reflection of the original graph across the x-axis is indicated as Graph B, which is marked with a checkmark.
![**Reflection of Function Graphs**
**Problem:**
Let \( g(x) \) be the reflection of \( f(x) \) across the \( x \)-axis. Which of the following graphs represents the graph of \( g(x) \)?
**Graph Explanations:**
- **Graph A:** Shows a curve in the first quadrant moving towards the negative \( y \)-axis in the third quadrant.
- **Graph B:** Displays a curve in the second quadrant with a negative slope moving upwards towards the positive \( y \)-axis in the first quadrant.
- **Graph C:** Depicts an upward-sloping curve starting from the negative \( x \)-axis moving into the first quadrant.
- **Graph D:** Exhibits an upward-sloping curve starting from the positive \( x \)-axis moving into the first quadrant.
**Correct Answer:** Graph B is checked as correct.
**Additional Questions:**
1. **What is the equation for \( g(x) \)?**
\( g(x) = \_\_\_\_\_\_ \) [help (formulas)]
2. **What is the \( y \)-intercept of \( g(x) \)? Enter an ordered pair for the intercept.**
\(\_\_\_\_\_\_\) [help (points)]
This section helps students understand how to identify the reflection of a function across the \( x \)-axis and reinforce learning through graphical analysis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F92752472-4d8c-40a4-8452-4066d437a7ee%2F6ff561cd-6f97-47f1-b249-38efeb14e351%2Fcz6cwfm_processed.png&w=3840&q=75)
Transcribed Image Text:**Reflection of Function Graphs**
**Problem:**
Let \( g(x) \) be the reflection of \( f(x) \) across the \( x \)-axis. Which of the following graphs represents the graph of \( g(x) \)?
**Graph Explanations:**
- **Graph A:** Shows a curve in the first quadrant moving towards the negative \( y \)-axis in the third quadrant.
- **Graph B:** Displays a curve in the second quadrant with a negative slope moving upwards towards the positive \( y \)-axis in the first quadrant.
- **Graph C:** Depicts an upward-sloping curve starting from the negative \( x \)-axis moving into the first quadrant.
- **Graph D:** Exhibits an upward-sloping curve starting from the positive \( x \)-axis moving into the first quadrant.
**Correct Answer:** Graph B is checked as correct.
**Additional Questions:**
1. **What is the equation for \( g(x) \)?**
\( g(x) = \_\_\_\_\_\_ \) [help (formulas)]
2. **What is the \( y \)-intercept of \( g(x) \)? Enter an ordered pair for the intercept.**
\(\_\_\_\_\_\_\) [help (points)]
This section helps students understand how to identify the reflection of a function across the \( x \)-axis and reinforce learning through graphical analysis.
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