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3. graph the following functions on the same coordinate plane given below and make sure you label each of your graphs with their correct function name:

a. graph the following absolute value function and show your work to determine the vertex: f(x) = |x - 3| + 1

b. the function g(x) translates f(x) 5 units up. graph the g(x) on the same coordinate plane and write the g(x) function.

c. the function h(x) reflects g(x) over the x-axis. graph the h(x) on the same coordinate plane and write the h(x) function.

A. (3,1)

B. g(x)=|x-3|+6

C. h(x)=-|x-3|-6

Step-by-step explanation:

A. To graph the absolute value function f(x) = |x - 3| + 1, first graph the parent absolute value function y=|x| and then translate it 3 units to the right and 1 unit up (see green graph in attached diagram). The vertex of the function f(x) is at point (3,1).

B.  The function g(x) translates f(x) 5 units up, so its equation is

g(x)=f(x)+5

g(x)=|x-3|+1+5

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

Blue graph in attached diagram.

C. The function h(x) reflects g(x) over the x-axis, so the equation of the function h(x) is

h(x)=-g(x)

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

h(x)=-|x-3|-6

Red graph in attached diagram.