Suppose that a function y = f(x) is increasing on the interval (-8, 5). (a) Over

Question

Suppose that a function y = f(x) is increasing on the interval (-8, 5). (a) Over what interval is the graph of y = f(x + 7) increasing? The graph of y = f(x + 7) is increasing over the interval (Type your answer in interval notation.) (b) Over what interval is the graph of y = f(x - 2) increasing? The graph of y = f(x - 2) is increasing over the interval (Type your answer in interval notation.) (c) What can be said about the graph of y = -f(x)? Choose the statement below that is true about y = f(x). The graph of y = -f(x) is decreasing on the interval (-8, 5). The graph of y = -f(x) is decreasing on the interval (-5, 8). The graph of y = -f(x) is increasing on the interval (-5, 8). The graph of y = -f(x) is increasing on the interval (-8, 5). (d) What can be said about the graph of y = f(-x)? Choose the statement below that is true about y = f(-x).

Explanation / Answer

       Suppose   that   a   function   y = f(x)    is   increasing on the   interval ( -8, 5 )

a )          Over   what Interval   is   the   graph   of     f(x+7) increasing .

               The     x + 7    is    offsetting   the   input    of     x .

               The   beginning    of    the    function   increase   is    at    x + 7 = - 8

                x = -15

                and    the   Ending    of    the   function   increase   is    at    x + 7 = 5

                x = -2

               Therefore , Graph   of    the   function    y = f(x+7)    is    increasing   over the

               Interval     ( -15 , -2 ) .

              

b )       Suppose   that   a   function   y = f(x)    is   increasing on the   interval ( -8, 5 )

              To   Find   Over   what   Interval   is    the Graph of     f(x-2)   increasing

            The     x - 2    is    offsetting   the   input    of     x .

               The   beginning    of    the    function   increase   is    at    x - 2 = - 8

                x = -6

             and    the   Ending    of    the   function   increase   is    at    x - 2 = 5

                x = 7

               Therefore , Graph   of   f(x-2)    is increasing on the Interval ( -6 , 7 )

       

c   )       What   can   be said   about   the   Graph    of    y = - f(x)

             To   Find   Over   what   Interval   is    the Graph of    -f(x) increasing

            The     -x is    offsetting   the   input    of     x .

             The   beginning    of    the    function   increase   is    at    -x = 8

              x = -8

             and    the   Ending    of    the   function   increase   is    at     -x = -5

              x = 5

             Therefore , Graph    of    the   function    is    Decreasing    at   ( -8 , 5)

             Hence, OPtion    B

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