Given
Original function:
[tex]f(x)\text{ = }\frac{1}{4}x^3\text{ -6}[/tex]
Given that:
[tex]g(x)\text{ =f(x}-3)\text{ + 10}[/tex]
We can find the expression for g(x) using the given rule:
[tex]\begin{gathered} g(x)\text{ = }\frac{1}{4}(x-3)^3-6\text{ + 10} \\ =\text{ }\frac{1}{4}(x-3)^3\text{ + 4} \end{gathered}[/tex]
Using a graphing calculator, we can graph f(x) and g(x) as shown below:
Hence, the correct option is Option C
Answer: Option C
