In both Parts I and II of this activity, your team will be assigned one of the four groups of functions (A, B, C or D). Work carefully and clearly, as you will be presenting the results of your function group to the rest of the class - who will have worked on different groups. Part I f(x)=x² f(x)=x² f(x)=x² g(x) = 2x² f(x)=x² g(x)=1/3x² g(x) = 3x² g(x) = -1/2x² A. h(x) = -2x² h(x) = -3x² 1 1 1 =-X" h(x) = h(x)= p(x) = p(x) p(x) = 2x² p(x)=-3x² For the function group you are assigned, simultaneously graph all three of the functions in an appropriate viewing window. How do the graphs of y=g(x) and y=h(x) compare to the graph of y=f(x)? Discuss your observations with your group members and answer the following questions. 1. Explain (write words!) how the graph of h(x) = -ax² compares to the graph of g(x) = ax². 2. Explain how the graph of g(x) = ax² compares to the graph of f(x) = x² when a>1. 2. Explain how the graph of g(x) = ax² compares to the graph of f(x)=x² if 0
In both Parts I and II of this activity, your team will be assigned one of the four groups of functions (A, B, C or D). Work carefully and clearly, as you will be presenting the results of your function group to the rest of the class - who will have worked on different groups. Part I f(x)=x² f(x)=x² f(x)=x² g(x) = 2x² f(x)=x² g(x)=1/3x² g(x) = 3x² g(x) = -1/2x² A. h(x) = -2x² h(x) = -3x² 1 1 1 =-X" h(x) = h(x)= p(x) = p(x) p(x) = 2x² p(x)=-3x² For the function group you are assigned, simultaneously graph all three of the functions in an appropriate viewing window. How do the graphs of y=g(x) and y=h(x) compare to the graph of y=f(x)? Discuss your observations with your group members and answer the following questions. 1. Explain (write words!) how the graph of h(x) = -ax² compares to the graph of g(x) = ax². 2. Explain how the graph of g(x) = ax² compares to the graph of f(x) = x² when a>1. 2. Explain how the graph of g(x) = ax² compares to the graph of f(x)=x² if 0
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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Transcribed Image Text:Math 096/140
Worksheet 4.2: Graphing Parabolas Team Activity
In both Parts I and II of this activity, your team will be assigned one of the four groups of
functions (A, B, C or D). Work carefully and clearly, as you will be presenting the results
of your function group to the rest of the class - who will have worked on different
groups.
Part I
f(x)=x²
f(x) = x²
g(x) = 2x²
f(x) = x²
g(x) = 3x²
1
f(x) = x²
g(x) = -x²
1
g(x)= x²
2
h(x) = −2x?
B. h(x)=-3x²
1
1
h(x) = - = x²
1
h(x) = -
= 1/2x²
=-=-3x²
p(x) =
p(x-.
r²
3
p(x) = 2x²
p(x)=-3x²
For the function group you are assigned, simultaneously graph all three of the functions
in an appropriate viewing window. How do the graphs of y=g(x) and y=h(x) compare
to the graph of y=f(x)? Discuss your observations with your group members and
answer the following questions.
1. Explain (write words!) how the graph of h(x) = -ax² compares to the graph of
g(x) = ax².
2. Explain how the graph of g(x) = ax² compares to the graph of f(x) = x² when
a>1.
2. Explain how the graph of g(x) = ax² compares to the graph of f(x) = x² if
0<a<1 (a is positive but less than 1.)
A.
C.
D.
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