Describe the transformations of f(x)=sqrt[3]{x} and h(x)=x^{3} that result in the functions listed below. g(x)= -sqrt[3]{x - 3} and j(x)= -(x - 3)^{3} p(x)=4sqrt[3]{-x} - 1 and q(x)=0.25(-4x)^{3} - 1

iohanetc 2020-11-01 Answered
Describe the transformations of
f(x)=3{x} and h(x)=x3
that result in the functions listed below.
g(x)= 3{x  3} and j(x)= (x  3)3
p(x)=43{x}  1 and q(x)=0.25(4x)3  1
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Expert Answer

broliY
Answered 2020-11-02 Author has 97 answers
Step 1
We are given the functions:
f(x)=3{x}
h(x)=x3
Step 2
a) We write the transformations of the function f(x) to reach g(x)= 3{x  3}:
3{x}  3{x  3} (shift to the right with 3 units)
3{x  3}   3{x  3} (reflection in the x-axis)
Step 3
We write the transformations of the function h(x) to reach j(x)= (x  3)3:
x3  (x  3)3 (shift to the right with 3 units)
(x  3)3  (x  3)3 (reflection in the x-axis)
Step 4
b). We write the transformations of the function f(x) to reach p(x)=43{x}  1:
3{x}  3{x} (reflection in the y-axis)
3{x}  43{x} (vertical strech)
43{x}  43{x} 1 (shift down with 1 unit)
Step 5
We write the transformations of the function h(x) to reach q(x)=0.24(4x)3 1:
x3  (4x)3 (horizontal shrink)
(4x)3  (4x)3 (reflection in they-axis)
(4x)3  0.25(4x)3 (vertical shrink)
0.25(4x)3  0.25(4x)3  1 (shift down with 1 unit)
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