Question

Write a formula for the function obtained when the graph is shifted as described. When typing exponents use the carrot key ^ by pressing SHIFT and 6. For example x squared can be typed as x^2. Do not put spaces between your characters and remember to use parentheses in the appropriate places!f(x)=|x| is shifted down 3 unit and to the right 1 units.The new equations f(x)=Answer

Answer 1

Remember the following transformation rules for functions:

Vertical translation up c units:

`f(x)\rightarrow f(x)+c`

Vertical translation down c units:

`f(x)\rightarrow f(x)-c`

Horizontal translation left c units:

`f(x)\rightarrow f(x+c)`

Horizontal translation right c units:

`f(x)\rightarrow f(x-c)`

If the given function, f(x)=|x| must be shifted down 3 units and to the right 1 unit, then, substract 3 from the function and substract 1 from the argument of the function.

First, perform a vertical translation down 3 units:

`|x|\rightarrow|x|-3`

Next, perform a horizontal translation right 1 unit:

`|x|-3\rightarrow|x-1|-3`

Therefore, the new equation is:

`f(x)=|x-1|-3`