Question

Write a formula for the function obtained when the graph is shifted as described. Use parentheses in appropriate places.

Answer 1

Given:

The function if given as,

$f(x)=x^2\text{ . . . .(1)}$

The objective is to write the formula for the transformations.

Explanation:

Reflection over the x-axis:

For the first transformation of reflection over the x-axis,

$\begin{gathered} f(x)=-f(x) \\ f(x)=-(x^2)\text{. . . . .(2)} \end{gathered}$

Shifting 13 units down:

Then, for shifting down 13 units down the equation will be,

$f(x)=f(x)-13$

Then, the equation (2) can be written as,

$f(x)=-(x)^2-13\text{ . . . . (3)}$

Shifting 4 units right:

For, shifting 4 units to the right the equation will be,

$f(x)=f(x-4)$

Then, the equation (3) can be written as,

$f(x)=-(x-4)^2-13\text{ }$

Hence, the equation of the transformed graph is f(x) = -(x-4)²-13.