Explanation:
Concept:
The function translation / transformation rules:
f (x) + b shifts the function b units upward.
f (x) − b shifts the function b units downward.
f (x + b) shifts the function b units to the left.
f (x − b) shifts the function b units to the right.
−f (x) reflects the function in the x-axis (that is, upside-down).
Th function of f(x) is given below as
[tex]f(x)=x^3-x+1[/tex]
To translate a function f(x) k units up to give g(x) , we will use the transformation rule below
[tex]g(x)=f(x)+k[/tex]
In this case,
The given functions and values are
[tex]\begin{gathered} f(x)=x^3-x+1 \\ k=3 \end{gathered}[/tex]
By substituting the values, we will have
[tex]\begin{gathered} g(x)=f(x)+k \\ g(x)=x^3-x+1+3 \\ g(x)=x^3-x+4 \end{gathered}[/tex]
Hence,
The final answers are
[tex]\begin{gathered} rule\Rightarrow g(x)=f(x)+3 \\ g(x)=x^3-x+4 \end{gathered}[/tex]
