Consider the power functions f(x) = cx - 2. Select the graphs of f versus x for c = 1, c = 2, c = 4, and c = 6. A table of values will be helpful in choosing a vertical span. On the basis of the plots you chose, discuss the effect of the coefficient c on a power function when the power is negative. The graph shows that larger values of c make the function
Consider the power functions f(x) = cx - 2. Select the graphs of f versus x for c = 1, c = 2, c = 4, and c = 6. A table of values will be helpful in choosing a vertical span. On the basis of the plots you chose, discuss the effect of the coefficient c on a power function when the power is negative. The graph shows that larger values of c make the function
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Consider the power functions f(x) = cx - 2.
Select the graphs of f versus x for c = 1, c = 2, c = 4, and c = 6. A table of values will be helpful in choosing a vertical span.
On the basis of the plots you chose, discuss the effect of the coefficient c on a power function when the power is negative.
The graph shows that larger values of c make the function
Transcribed Image Text:**Title: Understanding the Effects of Coefficient Changes in Power Functions**
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**Topic: Power Functions Analysis**
**Learning Objective:** Examine how varying the coefficient \( c \) in the power function \( f(x) = cx^{-2} \) influences the graph of the function for \( c = 1, c = 2, c = 4, \) and \( c = 6 \).
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**Instructions:**
Consider the power functions \( f(x) = cx^{-2} \).
**Task:** Select the graphs of \( f \) versus \( x \) for \( c = 1 \), \( c = 2 \), \( c = 4 \), and \( c = 6 \). Use the provided key to identify the lines representing each value of \( c \).
**Key:**
- \( c = 1 \) (black)
- \( c = 2 \) (red)
- \( c = 4 \) (blue)
- \( c = 6 \) (green)
### Graph Analysis:
**Top-left plot:**
- Depicts four curves decreasing from the top-left towards the bottom-right.
- The black curve (\( c = 1 \)) is the highest curve.
- The red curve (\( c = 2 \)), blue curve (\( c = 4 \)), and green curve (\( c = 6 \)) follow sequentially, showing an increasingly rapid descent as \( c \) increases.
**Top-right plot:**
- Shows four curves increasing from the bottom-left towards the top-right.
- The green curve (\( c = 6 \)) is the most rapid ascent.
- The blue curve (\( c = 4 \)), red curve (\( c = 2 \)), and black curve (\( c = 1 \)) follow, with decreasing steeper slopes.
**Bottom-left plot:**
- Similar to the top-left graph, depicting decreasing curves with the same order and colors indicating \( c = 1 \), \( c = 2 \), \( c = 4 \), and \( c = 6 \).
**Bottom-right plot:**
- Similar to the top-right graph, showing curves increasing with the same color sequence: black (\( c = 1 \)), red (\( c = 2 \)), blue (\( c = 4 \)), and green (\( c = 6 \)).
### Discussion:
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