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Below is the graph of y=e*. Transform it to make the graph of y=-e* +5. Give the domain and range of y=-e* +5 using interval notation. -8 Domain: Range: X (0,0) (0,0) (0,0) (0,0) OUD ?

Below is the graph of y=e*. Transform it to make the graph of y=-e* +5. Give the domain and range of y=-e* +5 using interval notation. -8 Domain: Range: X (0,0) (0,0) (0,0) (0,0) OUD ?

Calculus: Early Transcendentals
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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### Transformations and Interval Notation #### Instructions: Below is the graph of \( y = e^x \). 1. Transform it to make the graph of \( y = -e^x + 5 \). 2. Give the domain and range of \( y = -e^x + 5 \) using interval notation. #### Graph Explanation: The provided graph displays the standard exponential function \( y = e^x \), where the y-axis represents the output (y-values) and the x-axis represents the input (x-values). The curve shown is an increasing exponential line starting close to the x-axis on the left and rising steeply as x increases. #### Steps for Transformation: - To transform \( y = e^x \) to \( y = -e^x + 5 \), follow these steps: 1. Reflect the graph of \( y = e^x \) across the x-axis to get \( y = -e^x \). 2. Shift the graph of \( y = -e^x \) upward by 5 units to get \( y = -e^x + 5 \). ### Domain and Range in Interval Notation: 1. **Domain**: - The domain of \( y = e^x \) is all real numbers, \((-\infty, +\infty)\). - Since transformations do not affect the domain, the domain of \( y = -e^x + 5 \) remains the same. **Domain Interval Notation**: \( (-\infty, +\infty) \) 2. **Range**: - The original range of \( y = e^x \) is \((0, +\infty)\). - Reflecting it across the x-axis changes the range to \((- \infty, 0)\). - Shifting the graph up by 5 units alters the range to \((5 - \infty, 5)\). **Range Interval Notation**: \( (-\infty, 5) \) #### Graphical User Interface: - The user interface includes buttons for moving, rotating, and resetting graphs, as well as a help button. There are also fields to input the domain and range and some interval notation options for input selection. Make sure to use the information provided to correctly identify and input the domain and range of the transformed function \(
Transcribed Image Text:### Transformations and Interval Notation #### Instructions: Below is the graph of \( y = e^x \). 1. Transform it to make the graph of \( y = -e^x + 5 \). 2. Give the domain and range of \( y = -e^x + 5 \) using interval notation. #### Graph Explanation: The provided graph displays the standard exponential function \( y = e^x \), where the y-axis represents the output (y-values) and the x-axis represents the input (x-values). The curve shown is an increasing exponential line starting close to the x-axis on the left and rising steeply as x increases. #### Steps for Transformation: - To transform \( y = e^x \) to \( y = -e^x + 5 \), follow these steps: 1. Reflect the graph of \( y = e^x \) across the x-axis to get \( y = -e^x \). 2. Shift the graph of \( y = -e^x \) upward by 5 units to get \( y = -e^x + 5 \). ### Domain and Range in Interval Notation: 1. **Domain**: - The domain of \( y = e^x \) is all real numbers, \((-\infty, +\infty)\). - Since transformations do not affect the domain, the domain of \( y = -e^x + 5 \) remains the same. **Domain Interval Notation**: \( (-\infty, +\infty) \) 2. **Range**: - The original range of \( y = e^x \) is \((0, +\infty)\). - Reflecting it across the x-axis changes the range to \((- \infty, 0)\). - Shifting the graph up by 5 units alters the range to \((5 - \infty, 5)\). **Range Interval Notation**: \( (-\infty, 5) \) #### Graphical User Interface: - The user interface includes buttons for moving, rotating, and resetting graphs, as well as a help button. There are also fields to input the domain and range and some interval notation options for input selection. Make sure to use the information provided to correctly identify and input the domain and range of the transformed function \(
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