Mathematical Modeling Sec 6.8 – Characteristics of Functions Name: Consider the function can be defined by the set of ordered pairs m(x) What is the Domain: What is the Range: Given . Determine the Range of if the Domain is Given . Determine the Domain of if the Range is just the f(x) h(x) restricted to just set Describe the Domain, Range, Intervals of Increase/Decrease, End Behavior, Intercepts. A. Consider the following function. B. Consider the following function. i) Describe the Domain: i) Describe the Domain: ii) Describe the Range: ii) Describe the Range: iii) Describe iii) Describe Intervals of Increase: Intervals of Increase: iv) Describe Intervals of Decrease: iv) Describe Intervals of Decrease: v) As determine f(x) v) As determine f(x) x→∞, → x→∞, → vi) As determine f(x) vi) As determine f(x) x→ –∞, → x→ –∞, → vii) Determine the x-intercept: vii) List any local maximums: viii) Determine the y-intercept: viii) List any local minimums: ix) ix) on the Horizontal Asymptote: Average Rate of Change interval from = 3 to = 0 x x – A plumber charges $60 per hour and will only work a maximum of 8 hours on any given day. If we consider this situation a function where the number of hours worked, is the independent variable and how much the plumber charges in dollars, is the dependent x, y, variable. Determine the Domain and Range of the function. What is the Domain: What is the Range:
Sec 6.8 – Mathematical Modeling Characteristics of Functions Name: Consider the function m(x) can be defined by the set of ordered pairs What is the Domain: What is the Range: Given . Determine the Range of f(x) if the Domain is restricted to just Given . Determine the Domain of h(x) if the Range is just the set Describe the Domain, Range, Intervals of Increase/Decrease, End Behavior, Intercepts. A. Consider the following function. B. Consider the following function. i) Describe the Domain: i) Describe the Domain: ii) Describe the Range: ii) Describe the Range: iii) Describe Intervals of Increase: iii) Describe Intervals of Increase: iv) Describe Intervals of Decrease: iv) Describe Intervals of Decrease: v) As x→∞, determine f(x) → v) As x→∞, determine f(x) → vi) As x→ –∞, determine f(x) → vi) As x→ –∞, determine f(x) → vii) Determine the x-intercept: vii) List any local maximums: viii) Determine the y-intercept: viii) List any local minimums: ix) Horizontal Asymptote: ix) Average Rate of Change on the interval from x = – 3 to x = 0 A plumber charges $60 per hour and will only work a maximum of 8 hours on any given day. If we consider this situation a function where the number of hours worked, x, is the independent variable and how much the plumber charges in dollars, y, is the dependent variable. Determine the Domain and Range of the function. What is the Domain: What is the Range:
06-08-FunctionCharectristics-Blank.docx