Answer:
g(x)= (x+6)³ + 4
Step-by-step explanation:
A polynomial is an algebraic expression for ordered addition, subtraction, and multiplication made of variables, constants, and exponents. Its form is:
[tex]P(x)=a_{n} x^{n} +a_{n-1} x^{n-1} +a_{n-2} x^{n-2} +...+a_{2} x^{2} +a_{1} x+x_{0}[/tex]
where n is a natural number, [tex]a_{n} ,a_{n-1} ,a_{n-2} ,a_{2} ,a_{1} ,a_{0}[/tex] ar the coefficients and x is the variable.
In this case, the polynomial is:
f(x)=x³
When the function f (x) is translated into "x" and "y", where h is the translation in "x" and k is the translation in the "y" axis, this is expressed as f (x -h) + k. In this case:
g(x) = f (x -h) + k
g(x)= (x-h)³+k
You want to move the function 6 places to the left, that is, to the negative of the "x". So h is -6. And 4 units up, that is to say towards the positive of the "y". So k = 4. Replacing:
g(x)= (x-(-6))³ + 4
g(x)= (x+6)³ + 4
The corresponding graphs are seen in the attached image, where the function in red corresponds to f(x)=x³ and the function in blue corresponds to g(x)= (x+6)³ + 4
