Math

QuestionTranslate the function f(x)=xf(x)=|x| right 3 units and up 2 units.

Studdy Solution

STEP 1

Assumptions1. The function is f(x)=xf(x) = |x| . We need to translate the function right by3 units3. We need to translate the function up by units

STEP 2

The general form of a translated absolute function is f(x)=xh+kf(x) = |x - h| + k, where hh is the horizontal shift and kk is the vertical shift.

STEP 3

In our case, we need to shift the function to the right by3 units. This corresponds to a hh value of -3.f(x)=x(3)f(x) = |x - (-3)|

STEP 4

implify the equation.
f(x)=x+3f(x) = |x +3|

STEP 5

Now, we need to shift the function up by2 units. This corresponds to a kk value of2.
f(x)=x+3+2f(x) = |x +3| +2

STEP 6

The translated function is f(x)=x+3+2f(x) = |x +3| +2. This is the function f(x)=xf(x) = |x| translated3 units to the right and2 units up.
The solution is f(x)=x+3+2f(x) = |x +3| +2.

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