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Calculus I                                                          Quiz #3                            February 17, 2004

Name____________________                   R.  Hammack                              Score ______
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(1) This problem involves two functions. One function is f(x) = x^2 - x.
The other function g(x) is graphed below.

[Graphics:HTMLFiles/quiz3sol_4.gif]
(a)  f(g(2)) =f(2) = 2^2 - 2 = 2

(b)  g(f(-1)) =g((-1)^2 - (-1)) = g(2) = 2

(c) Using the coordinate axis above, sketch the graph of y = g(x) - 2
The graph of g(x) is just moved down 2 units, as illustrated.


(2)  Suppose f(x) = x^2 - x  and g(x) = 2x + 1

(a)  (f∘g) (x) =f(g(x)) = g(x)^2 - g(x) = (2x + 1)^2 - (2x + 1) = 4x^2 + 4x + 1 - 2x - 1 = 4x^2 + 2x

(b)  (g∘f) (x) =g(f(x)) = 2f(x) + 1 = 2 (x^2 - x) + 1 = 2x^2 - 2x + 1


(3) Find the equation of the line passing through the points (2, 4) and (1, -7).
Please put your final answer in slope-intercept form.

The slope will be m = (-7 - 4)/(1 - 2) = 11
Now, using point-slope form, we get
y - 4 = 11 (x - 2)
y - 4 = 11x - 22
y - 4 = 11x - 18