Question

Write the rule for the functiong(x) translate f(x)=x^3 -x+1 3 units up

Answer 1

Step-by-step 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

`f(x)=x^3-x+1`

To translate a function f(x) k units up to give g(x) , we will use the transformation rule below

`g(x)=f(x)+k`

In this case,

The given functions and values are

`\begin{gathered} f(x)=x^3-x+1 \\ k=3 \end{gathered}`

By substituting the values, we will have

`\begin{gathered} g(x)=f(x)+k \\ g(x)=x^3-x+1+3 \\ g(x)=x^3-x+4 \end{gathered}`

Hence,

The final answers are

`\begin{gathered} rule\Rightarrow g(x)=f(x)+3 \\ g(x)=x^3-x+4 \end{gathered}`