Section 1.4 - From Professor PDF

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Lecture Notes from the Professor ~ Extremely Helpful and Clear...

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Math 112 Lecture Notes Fall 2017 – Coach Dorff Section 1.4 – Sept 11, 2017 Preliminaries 1. Prayer. 2. ALEKS pretest: Need to have a score of 76 or higher by Wed Sept 13. 3. Add/Drop deadline is Tue Sept 12. If you got less than 76 on the ALEKS pretest, you do not remember the algebra skills needed to succeed in Math 112, and it is recommended that you transfer into Math 110. 4. Review Problem. (a) Find all values of x in [0, 2π] such that sin x = tan x. Solution:

sin x = tan x sin x =

sin x cos x

cos x sin x − sin x = 0 (sin x)(cos x − 1) = 0 sin x = 0 OR cos x = 1 ↓ ↓ x = 0, π, 2π OR x = 0, 2π

Answer: x = 0, π, 2π

Discussion 1. Laws of Exponents (a)

ax ay = ax+y

(b)

ax = ax−y ay

(c)

Examples: (a) Simplify (ax−1 )x+1 . (b) Simplify

a2 . a−4

2 −1

answer: ax

answer: a6

1

(ax )y = axy

(d)

(ab)x = ax bx

2. The graph of f (x) = ax : Notice ax > 0 1 since a0 = 1

a>1

0...