Answer:
Function g(x) is function f(x) vertically stretched by a factor of 6, reflected in the x-axis, and translated 2 units up.
Step-by-step explanation:
The graph of function f(x) is the parent function.
(Parent functions are the simplest form of a given family of functions).
The graph of g(x) is related to the graph of f(x) by a series of transformations. To determine the series of transformations, work out the steps of how to go from f(x) to g(x).
Step 1
Starting with the parent function x³, multiply by 6:
[tex]\implies 6f(x)=6x^3[/tex]
Therefore, this is a vertical stretch by a factor of 6.
Step 2
Now make 6x³ negative:
[tex]\implies -6f(x)=-6x^3[/tex]
Therefore, this is a reflection in the x-axis.
Step 3
Finally, add 2:
[tex]\implies -6f(x)+2=-6x^3+2[/tex]
Therefore, the function has been translated 2 units up.
Therefore, function g(x) is function f(x) vertically stretched by a factor of 6, reflected in the x-axis, and translated 2 units up.
Learn more about transformations here:
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