Question

Please keep as simple as possible

Answer 1

Answer:

f(x) = (X^3 +6) + 4

Step-by-step explanation:

to move left add +6 from inside the parenthesis

to move up add +4 outside of parenthesis

*since there were no parenthesis you add them*

Answer 2

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:

$P(x)=a_{n} x^{n} +a_{n-1} x^{n-1} +a_{n-2} x^{n-2} +...+a_{2} x^{2} +a_{1} x+x_{0}$

where n is a natural number, $a_{n} ,a_{n-1} ,a_{n-2} ,a_{2} ,a_{1} ,a_{0}$ 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