
(a)
Find the parent function f .
(a)

Answer to Problem 34E
For the function, g(x)=−12(x+1)3 the parent function is f(x)=x3 .
Explanation of Solution
To identify the parent function, strip all the arithmetic operations on the function to leave behind one higher order operation in just x.
So, remove the arithmetic operation of multiplication by -1/2 from the given funcion to get the parent function.
(b)
Find the sequence of transformation from f to g.
(b)

Answer to Problem 34E
The shape of g(x)=−12(x+1)3 is drawn reflected in the y-axis and then stretched by by 1/2 units.
Explanation of Solution
Given information: g(x)=−12(x+1)3 and f(x)=x3
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 .
The shape of is drawn reflected in the x-axis and then shifted by 10 units is the required sequence of transformations from f to g .
(c)
To sketch the graph of g .
(c)

Answer to Problem 34E
Explanation of Solution
Given g(x)=(x+3)3−10
Use the sequence of transformation to plot the graph of the function
Obtain the graph of g(x)=(x+3)3−10 .
The graph can be obtained using the graphing calculator as shown below:
(d)
To write g in terms of f
(d)

Answer to Problem 34E
g(x)=−12f(x)
Explanation of Solution
Given information: g(x)=−12(x+1)3 and f(x)=x3
Conclusion:
Multiply f(x) by -1/2to get g(x) in terms of f(x)
Chapter 1 Solutions
EBK PRECALCULUS W/LIMITS
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