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Unit 1 . Characteristics and Applications of Functions. Parent Function Checklist. Unit 1: Characteristics and Applications of Functions. Parent Function Checklist. Parent Function Checklist. Parent Function Checklist. Parent Function Checklist. Parent Function Checklist.

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unit 1

Unit 1

Characteristics and Applications of Functions

parent function checklist
Parent Function Checklist

Unit 1: Characteristics and Applications of Functions

function vocabulary
Function Vocabulary

Unit 1: Characteristics and Applications of Functions

increasing
Increasing
  • Picture/Example
  • Common Language: Goes up from left to right.
  • Technical Language: f(x) is increasing on an interval when, for any a and b in the interval, if a > b, then f(a) > f(b).
decreasing
Decreasing
  • Picture/Example
  • Common Language: Goes down from left to right.
  • Technical Language: f(x) is decreasing on an interval when, for any a and b in the interval, if a > b, then f(a) < f(b).
maximum
Maximum
  • Picture/Example
  • Common Language: Relative “high point”
  • Technical Language: A function f(x) reaches a maximum value at x = a if f(x) is increasing when x < a and decreasing when x > a. The maximum value of the function is f(a).
minimum
Minimum
  • Picture/Example
  • Common Language: Relative “low point”
  • Technical Language: A function f(x) reaches a minimum value at x = a if f(x) is decreasing when x < a and increasing when x > a. The minimum value of the function is f(a).
asymptote
Asymptote
  • Picture/Example
  • Common Language: A boundary line
  • Technical Language: A line that a function approaches for extreme values of either x or y.
odd function
Odd Function
  • Picture/Example
  • Common Language: A function that is symmetric with respect to the origin.
  • Technical Language: A function is odd iff f(-x) = -f(x).
even function
Even Function
  • Picture/Example
  • Common Language: A function that has symmetry with respect to the y-axis
  • Technical Language: A function is even iff f(-x)=f(x)
end behavior
End Behavior
  • Picture/Example
  • Common Language: Whether the graph (f(x)) goes up, goes down, or flattens out on the extreme left and right.
  • Technical Language: As x-values approach ∞ or -∞, the function values can approach a number (f(x)n) or can increase or decrease without bound (f(x)±∞).
heart medicine
Heart Medicine

Unit 1: Characteristics and Applications of Functions

slide21
1) Use a graphing calculator to find the maximum rate at which the patient’s heart was beating. After how many minutes did this occur?
  • 79.267 beats per minute
  • 1.87 minutes after the medicine was given
2 describe how the patient s heart rate behaved after reaching this maximum
2) Describe how the patient’s heart rate behaved after reaching this maximum.
  • The heart rate starts decreasing, but levels off.
  • The heart rate never drops below a certain level (asymptote).
slide23
3) According to this model, what would be the patient’s heart rate 3 hours after the medicine was given? After 4 hours?
  • 3 hours = 180 minutes  h(180) ≈ 60.4 bpm
  • 4 hours = 240 minutes  h(240) ≈ 60.3 bpm
slide24
4) This function has a horizontal asymptote. Where does it occur? How can it’s presence be confirmed using a graphing calculator?
  • Asymptote: h(x)=60
  • Scroll down the table and look at large values of x or trace the graph and look at large values of x.
  • The end behavior of the function is: As x  ∞, f(x)  60 and as x  -∞, f(x)  60
end behavior1
End Behavior

Unit 1: Characteristics and Applications of Functions

piecewise defined functions
Piecewise-Defined Functions

Unit 1: Characteristics and Applications of Functions

evaluate the function at the given values by first determining which formula to use
Evaluate the function at the given values by first determining which formula to use.
continuity
Continuity

Unit 1: Characteristics and Applications of Functions

slide40
2) Graph each function using a “decimal” window (zoom 4) to observe the different ways in which functions can lack continuity.