_________________________________________________________________________
Calculus I                                                  Quiz  #3                                    September 10, 2003

Name____________________           R.  Hammack                                         Score ______
________________________________________________________________________
(1) Values for two functions f(x) and g(x) are given in the table.   

x -3 -2 -1 0 1 2 3 f(x) 2 1 0 -1 -2 -1 0 g(x) -1 0 1 2 3 3 3

(a)   (f∘g) (-3) =    f ( g(-3)) = f(-1) = 0
(b)   (f∘g) (-2) =    f ( g(-2)) = f(0) = -1
(c)    f ( g(-1)) = f(1) = -2
(d)    f ( g(0)) =   f(2) = -1
(e)    f ( g(1)) =   f(3) = 0
(f)   f ( g(2)) =   f(3) = 0
(g)    f ( g(3)) =   f(3) = 0

(h)  Draw a rough sketch of the graph of y = f(g(x)).
From the above work, we get the following table, from which the graph can be plotted.
   x -3 -2 -1 0 1 2 3 f(g(x)) 0 -1 -2 -1 0 0 0
[Graphics:HTMLFiles/quiz3sol_20.gif]

(2) The graph of a function f(x) is given. Using the same coordinate axis, sketch the graph of y = f(x - 3) + 1.
In red is sketched y = f(x - 3);  In green is sketched y = f(x - 3) + 1.
[Graphics:HTMLFiles/quiz3sol_26.gif]

(3) Find the equation of the line that passes through the point (2,4) and is parallel to the line 3x + y = 3.
Please put your answer in the slope-intercept form.

First the equation  3x + y = 3, can be put in the form  y = -3x + 3, and from this you can tell its slope is -3.
So we are looking for a line of slope -3 and passing through the point (2,4). Using the point-solpe formula,
y - 4 = -3 (x - 2)
y - 4 = -3x + 6
y = -3x + 10