(a)
In Exercises 21−46, g is related to one of the parent functions described in Section 1.6.
(a) Identify the parent function f
(b) Describe the sequence of transformations from f to g
(c) Sketch the graph of g
(d) Use function notation to write g in terms of f
24. g(x) = -x3-1
Identify the parent function f
(a)
Answer to Problem 24E
The Parent function is f(x)=x3
Explanation of Solution
Given:
g(x) = -x3-1
Concept Used:
A Parent function is the function in the simplest form possible for a given family of functions that tends to preserve the properties and definition of the entire family.
Conclusion:
The Parent function is f(x)=x3
(b)
Describe the sequence of transformations from f to g
(b)
Answer to Problem 24E
The shape of f(x)=x3, but reflected upon y-axis and then shifted downwards by 1 unit.
Explanation of Solution
Given:
g(x) = -x3-1
and
f(x)=x3
Concept Used:
The sequence of transformations from f to g depicts the steps followed and the transformations used to reach from the Parent function f to g .
Conclusion:
The shape of f(x)=x3, but reflected upon y-axis and then shifted downwards by 1 unit is the required sequence of transformations from f to g .
(c)
Sketch the graph of g .
(c)
Answer to Problem 24E
Explanation of Solution
Given:
Concept Used:
We used the sequence of transformations to the plot the above graph.
Conclusion:
We thus obtain the graph for
(d)
Use function notation to write
(d)
Answer to Problem 24E
Explanation of Solution
Given:
Conclusion:
Chapter 1 Solutions
EBK PRECALCULUS W/LIMITS
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