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Miscellaneous Notes: Inverse Functions, Trig Graphs, and Log/Ln Properties, Study notes of Calculus

Birla Institute of Technology and ScienceCalculus

Notes on inverse functions, trigonometric graphs, and logarithmic properties. It covers the process of finding inverse functions, the properties of trigonometric graphs including amplitude, period, frequency, horizontal shift, and vertical shift, and the properties of logarithmic functions such as the change in base and the relationship between log and exponentiation. Additionally, it discusses the concept of horizontal asymptotes and their behavior as x approaches infinity.

Typology: Study notes

2012/2013

Uploaded on 01/31/2013

ekavia
ekavia 🇮🇳

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Chapter P Miscellaneous Notes
Inverse Functions
• Switch x & y and solve for y
• Example:
( )
2
1fx x= +
find
( )
1
fx
−
Trig Graphs
•
sin x
o Amplitude: 1 (center to peak)
o Period: 2π
•
( )
sina bx c d++
o a changes amplitude
o b changes period/frequency
o c changes horizontal shift
o d changes vertical shift
Log/Ln Properties
•
ln ln lna b ab+=
•
ln ln ln a
ab b
−=
•
ln ln
b
a ba=
Horizontal Asymptotes
• Behavior as
x→∞
• Write as linear equation y = constant

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Chapter P Miscellaneous Notes

Inverse Functions

  • Switch x & y and solve for y

• Example: ( )

2

f x = x + 1 find ( )

1 f x

−

Trig Graphs

  • sin x

o Amplitude: 1 (center to peak)

o Period: 2π

• a sin( bx + c )+ d

o a changes amplitude

o b changes period/frequency

o c changes horizontal shift

o d changes vertical shift

Log/Ln Properties

  • ln a + ln b =ln ab
  • ln ln ln

a a b b

  • ln ln

b a = b a

Horizontal Asymptotes

  • Behavior as x → ∞
  • Write as linear equation y = constant