Homework Help is Here – Start Your Trial Now!
Math
Calculus
Which of the following describes the graph of h(x) = -2(x+3)+4? 4 h(x) 2 -6 -5 4 -3 -2 2 3 4 5 10 6 7 8 9 * -4 6 -9 -8 - 4 -5 4 -8 -10 -14 -16 Ty 2 -2 -10 18 ---10 -12 -14 -16 1 2 3 4 h(z) 5 6 7 8 9

Which of the following describes the graph of h(x) = -2(x+3)+4? 4 h(x) 2 -6 -5 4 -3 -2 2 3 4 5 10 6 7 8 9 * -4 6 -9 -8 - 4 -5 4 -8 -10 -14 -16 Ty 2 -2 -10 18 ---10 -12 -14 -16 1 2 3 4 h(z) 5 6 7 8 9

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...
See similar textbooks
icon
Related questions
Question
**Question:** Which of the following describes the graph of \( h(x) = -2^{(x-3)} + 4 \)? **Graphs:** 1. **First Graph:** - The graph consists of a curve that starts from the top-left corner, decreasing rapidly as it moves to the right. - It shows a near-vertical descent and gradually flattens out as it approaches \( y = -16 \) at \( x = 9 \). - The curve closely follows the y-axis below before turning towards the right. 2. **Second Graph:** - The graph begins from the bottom-left corner and moves upwards to the right. - Initially, the curve rises steeply and then starts to flatten out as it progresses rightwards. - The curve approaches but does not appear to cross \( y = 4 \) as it continues to move to the right. This suggests a horizontal asymptote at \( y = 4 \). - The graph levels off near \( y = 4 \) as \( x \) moves beyond \( 9 \), exemplifying the behavior of the exponential function \( -2^{(x-3)} + 4 \). **Explanation:** The graphs provided are to be analyzed to determine which one correctly represents the function \( h(x) = -2^{(x-3)} + 4 \). The second graph suits the characteristics of this exponential function since it reflects the behavior expected — rapidly increasing and asymptotically approaching \( y = 4 \) from below.
Transcribed Image Text:**Question:** Which of the following describes the graph of \( h(x) = -2^{(x-3)} + 4 \)? **Graphs:** 1. **First Graph:** - The graph consists of a curve that starts from the top-left corner, decreasing rapidly as it moves to the right. - It shows a near-vertical descent and gradually flattens out as it approaches \( y = -16 \) at \( x = 9 \). - The curve closely follows the y-axis below before turning towards the right. 2. **Second Graph:** - The graph begins from the bottom-left corner and moves upwards to the right. - Initially, the curve rises steeply and then starts to flatten out as it progresses rightwards. - The curve approaches but does not appear to cross \( y = 4 \) as it continues to move to the right. This suggests a horizontal asymptote at \( y = 4 \). - The graph levels off near \( y = 4 \) as \( x \) moves beyond \( 9 \), exemplifying the behavior of the exponential function \( -2^{(x-3)} + 4 \). **Explanation:** The graphs provided are to be analyzed to determine which one correctly represents the function \( h(x) = -2^{(x-3)} + 4 \). The second graph suits the characteristics of this exponential function since it reflects the behavior expected — rapidly increasing and asymptotically approaching \( y = 4 \) from below.
The image contains two graphs, each displaying a function \( h(x) \). #### First Graph (Top): - **Axes**: - The horizontal axis (x-axis) ranges from -9 to 9. - The vertical axis (y-axis) ranges from -16 to 2. - **Function**: \( h(x) \) - **Behavior**: - As \( x \) increases from left to right, the value of \( h(x) \) decreases sharply, continuing into the negative \( y \) values. - The graph appears to taper off more sharply as \( x \) becomes more positive, suggesting a steep decline. #### Second Graph (Bottom): - **Axes**: - The horizontal axis (x-axis) ranges from -9 to 9. - The vertical axis (y-axis) ranges from -16 to 2. - **Function**: \( h(x) \) - **Behavior**: - As \( x \) increases from left to right, the value of \( h(x) \) increases sharply from large negative \( y \) values to higher \( y \) values. - The graph shows a steep incline as \( x \) becomes more positive. ### Comparison: - Both graphs feature the same function, \( h(x) \), observed over a consistent range for \( x \) and \( y \) values. ### Purpose: These graphs can be used to illustrate different behaviors of a mathematical function, such as exponential decay in the first graph and exponential growth in the second graph. They serve as excellent visuals for understanding how function transformations reflect over the y-axis or around different points.
Transcribed Image Text:The image contains two graphs, each displaying a function \( h(x) \). #### First Graph (Top): - **Axes**: - The horizontal axis (x-axis) ranges from -9 to 9. - The vertical axis (y-axis) ranges from -16 to 2. - **Function**: \( h(x) \) - **Behavior**: - As \( x \) increases from left to right, the value of \( h(x) \) decreases sharply, continuing into the negative \( y \) values. - The graph appears to taper off more sharply as \( x \) becomes more positive, suggesting a steep decline. #### Second Graph (Bottom): - **Axes**: - The horizontal axis (x-axis) ranges from -9 to 9. - The vertical axis (y-axis) ranges from -16 to 2. - **Function**: \( h(x) \) - **Behavior**: - As \( x \) increases from left to right, the value of \( h(x) \) increases sharply from large negative \( y \) values to higher \( y \) values. - The graph shows a steep incline as \( x \) becomes more positive. ### Comparison: - Both graphs feature the same function, \( h(x) \), observed over a consistent range for \( x \) and \( y \) values. ### Purpose: These graphs can be used to illustrate different behaviors of a mathematical function, such as exponential decay in the first graph and exponential growth in the second graph. They serve as excellent visuals for understanding how function transformations reflect over the y-axis or around different points.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS