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IF.4: Parent Functions and their Characteristics

October 20 th , 2014. IF.4: Parent Functions and their Characteristics. Vocabulary. inputs. outputs. Domain: The value that is the ________in a function or relation. Range :  The set of all possible _________ of a function.

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IF.4: Parent Functions and their Characteristics

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  1. October 20th, 2014 IF.4: Parent Functions and their Characteristics

  2. Vocabulary inputs outputs Domain: The value that is the ________in a function or relation. Range: The set of all possible _________ of a function. x-intercept: The point where a line meets or crosses the _______ y-intercept: The point where a line meets or crosses the _______ Interval of Increasing: the domain (x-values) over which a function is ______________ Interval of Decreasing: the domain (x-values) over which a function is ______________ x-axis y-axis increasing decreasing

  3. Vocabulary lowest Minimum: the ____________ point on a graph Maximum: the ____________ point on a graph Rate of Change: the rate at which a function is ______________ or______________ (constant) How do you tell if a graph is positive? ________ the x-axis How do you tell if a graph is negative? _______the x-axis highest increasing decreasing above below

  4. Example 1: Consider the graph . Identify the following properties for the graph of the function . Domain: all real numbers Range: y > 0 x-intercept: None y-intercept: (0, 1) Interval of Increasing: all real #s or Interval of Decreasing: None Minimum or Minimum: None Positive: all real numbers Negative: never

  5. Example 2: Consider the function f(x) = x. Graph the functions below. This is known as the parent function of a linear equation.

  6. Identify the following properties for the graph of the function f(x) = x. Interval of Increasing: as x increases, f(x) increases Interval of Decreasing: as x decreases, f(x) decreases Minimum or Minimum: None Positive: x > 0 Negative: x < 0 Domain: all real numbers Range:all real numbers x-intercept: (0, 0) y-intercept: (0, 0)

  7. Example 3: Consider the function f(x) = -x. Graph the functions below. Interval of Increasing: as x increases, f(x) decreases Interval of Decreasing: as x decreases, f(x) increases Minimum or Minimum: None Positive: x < 0 Negative: x > 0 Domain: all real numbers Range:all real numbers x-intercept: (0, 0) y-intercept: (0, 0)

  8. Example 4: A company uses the function to represent the depreciation of a truck, where V is the value of the truck and x is the number of years after its purchase. Use the table of values shown below. What is the y-intercept of the graph of the function? From the table, when x = 0, V(x) = 28,000. So, (0, 28000) Does the graph of the function have an x-intercept? There is not one on the table, but could we find one? YES! For the x-intercept, V(x) = 0, so: Does the function increase or decrease? Decrease Why?

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