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A review sheet for Chapter 1 of MA 161, focusing on functions. It includes true or false questions, simplification problems, equation solving, and finding inverse functions. It also covers algebraic concepts such as finding the domain, function composition, and finding equations of lines.
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1 ๐ฅ 4
1 ๐ฅ 2 +
1 ๐ฅ 2
1 4
โ
(^2) โ
3
3
3
(a) f (x) = 3x + 7
f (x + h) = 3(x + h) + 7 = 3x + 3h + 7
f (x + h) f (x) = (3x + 3h + 7) (3x + 7) = 3h f (x + h) f (x) h
3 h h
(b) f (x) = x 2
f (x + h) = (x + h) 2 = x 2 + 2xh + h 2 f (x + h) f (x) = (x 2 + 2xh + h 2 ) (x 2 ) = 2xh + h 2 f (x + h) f (x) h
2 xh + h 2 h
h(2x + h) h = 2x + h
(c) f (x) = (^) x^1 +
f (x + h) =
(x + h) + 3
x + h + 3
f (x + h) f (x) =
x + h + 3
x + 3
(x + 3) (x + h + 3)(x + 3)
(x + h + 3) (x + h + 3)(x + 3)
=
(x + 3) (x + h + 3) (x + h + 3)(x + 3)