For each function in Exercises 1–4, evaluate (a) f ( 0 , 0 ) ; (b) f ( 1 , 0 ) ; (c) f ( 0 , − 1 ) ; (d) f ( a , 2 ) ; (e) f ( y , x ) ; and (f) f ( x + h , y + k ) ; [Hint: See Quick Examples 1–3. ] f ( x , y ) = x 2 + y 2 − x + 1
For each function in Exercises 1–4, evaluate (a) f ( 0 , 0 ) ; (b) f ( 1 , 0 ) ; (c) f ( 0 , − 1 ) ; (d) f ( a , 2 ) ; (e) f ( y , x ) ; and (f) f ( x + h , y + k ) ; [Hint: See Quick Examples 1–3. ] f ( x , y ) = x 2 + y 2 − x + 1
In Exercises 13-14, find the domain of each function.
13. f(x) 3 (х +2)(х — 2)
14. g(x)
(х + 2)(х — 2)
In Exercises 15–22, let
f(x) = x? – 3x + 8 and g(x) = -2x – 5.
Suppose f and g are the piecewise-defined functions defined
here. For each combination of functions in Exercises 51–56,
(a) find its values at x = -1, x = 0, x = 1, x = 2, and x = 3,
(b) sketch its graph, and (c) write the combination as a
piecewise-defined function.
f(x) = {
(2x + 1, ifx 0
g(x) = {
-x, if x 2
8(4):
51. (f+g)(x)
52. 3f(x)
53. (gof)(x)
56. g(3x)
54. f(x) – 1
55. f(x – 1)
Exercises 3 and 4: Write f(x) in the general form
f(x) = ax? + bx + c, and identify the leading coefficient.
3. f(x) = -2(x – 5)² + 1
4. f(x) = }(x + 1) - 2
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