1825_Sept29_notes_part2

# 1825_Sept29_notes_pa - MTH 1825 sec. 006    Wednesday, Sept. 29, 2010

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Unformatted text preview: MTH 1825 sec. 006    Wednesday, Sept. 29, 2010    Example:  Find the domain of each of the following functions.  Write your final answer in  interval notation.    f ( x) = x + 5     g( x ) = 3 x 2 − 10   a.        b.        € €    x+3 c.           d.  k( x) = x   h( x ) = x −5       € €      3x − 1 e.           f.  m( x ) = 2 x − 5   j( x) = 4x + 7       € €        x−4 g.  p( x ) = 2           h.  r( x ) = 12 − x   x +1     €   €        Section 2.7 – Graphs of Basic Functions    Linear and Constant Functions    A linear function is a function that can be written in the form  f ( x ) = mx + b , where  m ≠ 0 .  A constant function is a function that can be written in the form  f ( x ) = b .    The graphs of linear and constant functions are lines.  (A constant function is a horizontal  € € line.)  Why isn’t a vertical line a linear function?  €     Page 5 of 7  MTH 1825 sec. 006    Wednesday, Sept. 29, 2010    Graphs of Basic Functions                        Identity function:   f ( x ) = x       D:      R:      €                       Cubic function:   f ( x ) = x 3       D:      R:      €                       D:            Quadratic function:   f ( x ) = x 2   D:    €   R:          Absolute Value Function:   f ( x ) = x   D:      € R:  Square Root Function:   f ( x ) = x         € R:            Reciprocal Function:   f ( x ) = D:      R:  1   x € Page 6 of 7  MTH 1825 sec. 006    Wednesday, Sept. 29, 2010    A quadratic function is a function that can be written in the form:  f ( x ) = ax 2 + bx + c   where a, b, and c are real numbers and  a ≠ 0 .    Example:  Identify whether the function is constant, linear, quadratic, or none of these.    € 2 2 1 a.   f ( x ) = x − 7   b.   f ( x ) = c.   f ( x ) = π − 2   d.   f ( x ) = x 2 − 5 x + 3   − 7  5 5x 2       € € €     Finding the x­ and y­ intercepts of a function defined by y = f(x)    Given a function defined by  y = f ( x ) :    The y‐intercept is  f (0) .  The x‐intercept(s) are the real solutions to the equation  f ( x ) = 0 .  €   Example:  Find the intercepts of  f ( x ) = 3 x − 6 .  €   €     €         Example:  For the function  y = f ( x )  in the graph:    a.  Find  f (0) .    y = f ( x)   €     Which type of intercept did you find?  €   €       b.  Find the values for which  f ( x ) = 0 .        €   Which type of intercept did you find?          Page 7 of 7  € € ...
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## This note was uploaded on 11/06/2010 for the course MTH 1835 taught by Professor Cioni during the Fall '10 term at Michigan State University.

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