67. Exploration Graph y = x. Then on the same screen graph y = (x - 2)², followed by y = (x – 4)2, followed by y = (x + 2)². What pattern do you observe? Can you predict the graph of y = (x + 4)2? Of y = (x- 5)??

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Exponential And Logarithmic Functions
Section5.4: Exponential And Logarithmic Equations
Problem 83E: The number N of beavers in a given area after x years can be approximated by N=5.5100.23x,0x10. Use...
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Help me please with 67,72
D(33
t)
1.79 s vs 20
8 ft
22.04
33 – 1.5958 (33 – t)
v > 20
65. Challenge Problem Find the sum function (f + g) (x) if
where v represents the wind speed (in meters per second)
and t represents the air temperature (°C). Compute the
wind chill for the following:
2x + 3
if x < 2
f(x)
12+5x if xN 2
(a) An air temperature of 10°C and a wind speed of 1 meter
per second (m/sec)
and
(-4x + 1 ifxs0
g(x) =
if x >0
Explaining Concepts: Discussion and Writing
In Problems 66-73, use a graphing utility.
66. Exploration Graph y = x. Then on the same screen
71. Exploration Graph y = x'. Then on the same screen
graph y = (x 1)' + 2. Could you have predicted the
y = x² + 2, followed by y = x² + 4, followed
graph
by y = x² – 2. What pattern do you observe? Can you
predict the graph of y = x² – 4? Of y = x² + 5?
result?
72. Exploration Graph y = x, y = x*, and y
screen. What do you notice is the same about each graph?
What do you notice is different?
= x° on the same
67. Exploration Graph y = x. Then on the same screen
73. Exploration Graph y = x', y = x, and y = x' on the same
am screen. What do you notice is the same about each graph?
What do you notice
(x - 2)², followed by y = (x - 4)2, followed
graph y
by y = (x + 2)². What pattern do you observe? Can you
predict the graph of y = (x + 4)2? Of y = (x - 5)2?
68. Exploration Graph y = |x|. Then on the same screen
mo
different?
74. Consider the equation
if x is rational
graph y
2|x|, followed by y = 4|x|, followed by y =
y =
0 ifxis irrational
What pattern do you observe? Can you predict the graph of
Is this a function? What is its domain? What is its range?
What is its y-intercept, if any? What are its x-intercepts, if
any? Is it even, odd, or neither? How would you describe
its graph?
y = |? Of y = 5|x|?
69. Exploration Graph y = x. Then on the same screen
graph y = -x². Now try y = |x and y = -|x|. What do
you conclude?
75. Define some functions that pass through (0,0)
and (1, 1) and are increasing for x 0. Begin your list with
70. Exploration Graph y = Vx. Then on the same screen
graph y
VI, y =
= x, and y = x. Can you propose a general
V-x. Now try y = 2x + 1 and y = 2(-x) + 1.
y =
result about such functions?
Transcribed Image Text:D(33 t) 1.79 s vs 20 8 ft 22.04 33 – 1.5958 (33 – t) v > 20 65. Challenge Problem Find the sum function (f + g) (x) if where v represents the wind speed (in meters per second) and t represents the air temperature (°C). Compute the wind chill for the following: 2x + 3 if x < 2 f(x) 12+5x if xN 2 (a) An air temperature of 10°C and a wind speed of 1 meter per second (m/sec) and (-4x + 1 ifxs0 g(x) = if x >0 Explaining Concepts: Discussion and Writing In Problems 66-73, use a graphing utility. 66. Exploration Graph y = x. Then on the same screen 71. Exploration Graph y = x'. Then on the same screen graph y = (x 1)' + 2. Could you have predicted the y = x² + 2, followed by y = x² + 4, followed graph by y = x² – 2. What pattern do you observe? Can you predict the graph of y = x² – 4? Of y = x² + 5? result? 72. Exploration Graph y = x, y = x*, and y screen. What do you notice is the same about each graph? What do you notice is different? = x° on the same 67. Exploration Graph y = x. Then on the same screen 73. Exploration Graph y = x', y = x, and y = x' on the same am screen. What do you notice is the same about each graph? What do you notice (x - 2)², followed by y = (x - 4)2, followed graph y by y = (x + 2)². What pattern do you observe? Can you predict the graph of y = (x + 4)2? Of y = (x - 5)2? 68. Exploration Graph y = |x|. Then on the same screen mo different? 74. Consider the equation if x is rational graph y 2|x|, followed by y = 4|x|, followed by y = y = 0 ifxis irrational What pattern do you observe? Can you predict the graph of Is this a function? What is its domain? What is its range? What is its y-intercept, if any? What are its x-intercepts, if any? Is it even, odd, or neither? How would you describe its graph? y = |? Of y = 5|x|? 69. Exploration Graph y = x. Then on the same screen graph y = -x². Now try y = |x and y = -|x|. What do you conclude? 75. Define some functions that pass through (0,0) and (1, 1) and are increasing for x 0. Begin your list with 70. Exploration Graph y = Vx. Then on the same screen graph y VI, y = = x, and y = x. Can you propose a general V-x. Now try y = 2x + 1 and y = 2(-x) + 1. y = result about such functions?
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