For each function, do the following: a) state the name of the function, b) identify the independent and dependent variable, c) identify the rule that assigns exactly one output to the very input, and d) evaluate the function for the given input value.

Given the function in the question

f(x) = |x-3| + 2

a) state the name of the function

  Absolute value function

  since it is similar to f(x) = |x|

b) identify the independent and dependent variable  

x = independent variable (input variable)

f(x) or y = dependent variable  (output variable)

The variable which we assign the value we call the independent variable,    and the other variable is the dependent variable, since it value depends on  the independent variable.

c) identify the rule

A function is an equation that has only one answer for y for every x.

d) evaluate the function

given x = -5

 f(-5) = |-5 - 3| + 2

        = |-8| + 2

        = 8 +2

        = 10

a) y = -3x +2

b) y = 1/2x -6

these 2 can be combined into one equation.

-3x +2 = .5x -6

8 = 3.5x

x = 8 / 3.5 = 2.2857142857

y = -3 * (8 / 3.5) +2

y = (-24 / 3.5) + 2

y = -4.8571428571

step-by-step explanation: