Question

Describe the transformations to the absolute value toolkit function. ()=(1/2)|−3|+1Shrunk vertically by a factor of 2, translated left 3 units, and translated up 1 unit.Shrunk vertically by a factor of 2, translated right 3 units, and translated up 1 unit.Stretched vertically by a factor of 2, translated left 3 units, and translated up 1 unit.Stretched vertically by a factor of 2, translated right 3 units, and translated up 1 unit.

Answer 1

The parent function of f(x) is the absolute value function: g(x) = |x|.

From this function, the value of x was decreased by 3 units, so we have a horizontal translation of 3 units to the right.

$g^{\prime}(x)=g(x-3)=|x-3|$

Then, the value of the function was multiplied by the factor 1/2, which means a vertical shrunk by a factor of 2:

$g^{\prime}^^{\prime}(x)=\frac{1}{2}g^{\prime}(x)=\frac{1}{2}|x-3|$

And finally, the value of the function increased by 1 unit, which means a vertical translation of 1 unit up:

$f(x)=g^{\prime}^{\prime}(x)+1=\frac{1}{2}|x-3|+1$

Therefore the correct option is the second one.