Chapter 11 Flashcards

0
Q

Inverse of f(x)

A

F-1(x)

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1
Q

One-to-one function

A

In a one-to-one function, each x value corresponds to only one y value and each y value corresponds to only one x value

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2
Q

Inverse function

A

If (x,y) is in function f, then (y,x) is in the inverse of function f. The domain of a function is the range of its inverse, and the range of a function is the domain of its inverse.

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3
Q

Horizontal line test

A

Used on graphs to determine if a function is one-to-one

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4
Q

Find the inverse of f(x)=2x-6

A

F-1(x)= (x+6)/2

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5
Q

Exponential function

A

F(x)=a^x

A is greater than 0 and not 1, for all real numbers x

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6
Q

Domain of an exponential function

A

All real numbers

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7
Q

Range of exponential functions

A

(0, infinity)

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8
Q

Property for solving exponential equations

A

A is positive and not 1:

If A^x=A^y, then x=y

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9
Q

Compound interest formula

A

A(t)=P(1+r/n)^nt

A: amount investment is worth after t years
P: principal investment
r: interest rate
n: number of times per year that the interest in compounded

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10
Q

Exponential growth/decay formula

A

P(t)=Pe^rt
P(t): growth or decay after t years
P: original amount
r: growth/decay rate

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11
Q

Logarithmic form

A

Y=log. x
a

Y= exponent
a: base
X:a^y

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12
Q

Convert log. 32=5 to exponential form

2

A

2^5=32

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13
Q

Exponential form

A

X=a^y

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14
Q

Meaning of log. x

A

A

The exponent to which base a must be raised to obtain x

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15
Q

Log. b=?

b

16
Q

Log. 1=?

b

17
Q

Logarithmic function

A

G(x)=log. x

a

18
Q

Product rule of logarithms

A

Log. xy= log. x+log. y

b. b. b

19
Q

Quotient rule of logarithms

A

Log. X/y= log. X-log. y

b. b. b

20
Q

Power rule of logarithms

A

Log. X^r=rlog. X

b. b

21
Q

B^(log. X)=?

B

22
Q

Log. B^x=?

X

23
Q

Common log

A

Log x is written as logx

10

24
Natural log
Log. X is written as lnx | e
25
If x=y, then...
B^x=B^y
26
If b^x=b^y, then...
x=y
27
If x=y, then...
Log. X=log. Y | b. b
28
If log. X=log. Y, then... | b. b
X=y
29
Change of base formula
Log. X= (log. X)/(log a) | a. b. b