Pre calculus HW

Question

A function f is given, and the indicated transformations are applied to its graph (in the given order). Write the equation for the final transformed graph.

f(x) = |x|;

reflect in the x-axis, shift 3 units to the right, and shift upward 6 units

Answer 1

I will show these one at a time being added to the equation.

f(x) = |x| parent

f(x) = -|x| reflect on the x-axis

f(x) = -|x-3| shift 3 units to the right

f(x) = -|x-3|+6 shift upward 6 units

f(x) = -|x-3|+6