Question

What is the equation of the function S(x) = x4 translated horizontally 3 units to the right?What transformation of the function f(x) = x3 is shown by the equation f(x) = (x − 2)³

Answer 1

$\begin{gathered} S(x)=\text{ x}^4 \\ f(x)=x^3 \\ \text{ }\downarrow \\ f(x)=\text{ \lparen x-2\rparen}^3 \end{gathered}$

Required:

1. Translation of S(x) by 3 units horizontally toward the right

2. Transformation of F(x)

Explanation:

1. For translating toward the right we have to add 3 in the equation which will become

$S(x)=x^4+3$

2. In f(x) we are reducing the x so the value of f(x) will become less. So the whole graph will shift toward the y-axis from both the positive and negative sides.

Final Answer:

1.

$S(x)=x^4+3$

2. In f(x) we are reducing the x so the value of f(x) will become less. So the whole graph will shift toward the y-axis from both the positive and negative sides.