A Library of Parent Functions

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					A Library of Parent
Functions
 Section 2.4
 College Algebra, MATH 171
 Mr. Keltner
This Section
• The goal of this section is to make you able
  to recognize the basic shapes of the graphs
  of different types of functions.
   For instance, you know the graph of a linear
    function in the form f(x) = ax + b is a line with
    slope m = a and a y-intercept at (0, b).
   There are additional general shapes of graphs
    that we will investigate further.
Linear Functions
• The graph of a linear function has the following
  characteristics:
    The domain is the set of all real numbers, of (-∞, ∞).
    The range of the function is the set of all real numbers,
     or (-∞, ∞).
    The graph has an x-intercept at (-b/m, 0) and a y-
     intercept at (0, b).
    The graph is increasing if m>0 (positive) and
     decreasing if m<0 (negative).
Special Linear Functions
• There are two special types of linear
  functions:
   Constant functions, f(x) = c, which is a
    horizontal line
   Identity function, f(x) = x, which is a 45°
    angle, where the x- and y-coordinates are equal)
• Example 1: Write the linear function f for
  which f(0) = -1 and f(5) = 8.
Squaring Functions
• A squaring function is one of the form f(x) = x2.
    The domain is the set of all real numbers of (-∞, ∞).
    The range is the set of all nonnegative real numbers [0,
     ∞).
    Is an even function, where f(-x) = f(x).
    Has an intercept at (0, 0)
    Decreasing for (-∞, 0), increasing for (0, ∞).
    Symmetric to the y-axis (characteristic of an even
     function)
    Relative minimum at (0, 0)
Cubic Functions
• A cubic function is of the form f(x) = x3 and has
  the following characteristics:
    The domain is the set of all real numbers, of (-∞, ∞).
    The range of the function is the set of all real numbers,
     or (-∞, ∞).
    Is an odd function, where f(-x) = -f(x).
    Has an intercept at (0, 0)
    Increasing for (-∞, ∞).
    Symmetric with respect to the origin (characteristic of
     an even function)
Square Root Functions
• A square root function is of the form
  f(x) = √x.
   The domain of the function is the set of all
    nonnegative real numbers, [0, ∞).
   The range of the function is the set of all
    nonnegative real numbers, [0, ∞).
   The graph has an intercept at (0, 0).
   The graph is increasing on the interval (0,
    ∞).
Assessment
 Pgs. 220-221:
 #’s 5-60, multiples of 5

				
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