Math 3 Ch. 04.2 Log Functions

Front 1

The inverses of exponential functions are called:

Back 1

logarithmic functions

Front 2

The inverse of the function f(x) = aˣ is:

Back 2

logₐ(x)

Front 3

logₐ(x) is read:

Back 3

"log of x with base a"

Front 4

the expression of logₐ(x) is called:

Back 4

a logarithm

Front 5

In general, log of x with base a =

Back 5

the exponent that is used on the base a to obtain the value x.

Front 6

What is the inverse of this function? f(3) = 2³ = 8

Back 6

log₂(8) = 3

Front 7

What is the definition of a log function?

Back 7

For a > 0 and a ≠ 1, the logarithmic function with base a is denoted f(x) = logₐ(x), where logₐ(x) = y, IFF aʸ = x

Front 8

What is the domain and range of the logarithmic function f(x) = logₐ(x)?

Back 8

Since the function f(x) = logₐ(x) is the inverse of the function f(x) = aˣ, the Domain = (0,∞); the Range = (-∞,∞)

Front 9

There are no logarithms of:

Back 9

negative numbers or zero; meaning: no "log of -x with base a" or "log of 0 with base a."

Front 10

Expressions such as log₂(-4) and log₃(0) are:

Back 10

undefined

Front 11

logₐ(1) =

Back 11

0 for any base a, because a⁰ = 1 for any base a.

Front 12

What two bases are used more frequently than others?

Back 12

base 10 and base e.

Front 13

How are log₁₀(x) and logₑ(x) abbreviated?

Back 13

log₁₀(x) is abbreviated: log(x)
and logₑ(x) is abbreviated: ln(x)

Front 14

The Common Logarithmic function is denoted as:

Back 14

f(x) = log(x), where log(x) = y IFF 10ʸ = x

Front 15

The Natural Logarithmic function is denoted as:

Back 15

f(x) = ln(x), where ln(x) = y IFF eʸ = x

Front 16

The graph of y = aˣ has the __ -axis as its ____asymptote.

Back 16

The graph of y = aˣ has the x-axis as its horizontal asymptote.

Front 17

The graph of y = logₐ(x) has the __ -axis as its ____asymptote.

Back 17

The graph of y = logₐ(x) has the y-axis as its vertical asymptote.

Front 18

The function y = logₐ(x) is increasing if _______ and
decreasing if:

Back 18

The function y = logₐ(x) is increasing if a > 1
decreasing if a is between 0 and 1.

Front 19

The logarithmic function f(x) = logₐ(x) has the following properties:

Back 19

1) The function f is increasing for a > 1 and decreasing for 0 < a < 1.
2) The x-intercept of the graph of f is (1, 0).
3) The graph has the y-axis as a vertical asymptote.
4) The domain of f is (0, ∞); the range is (-∞,∞)
5) The function is one-to-one.
6) The functions f(x) = logₐ(x) and f(x) = aˣ are inverse functions.

Front 20

The logarithmic family of functions is in the form:

Back 20

g(x) = b • logₐ(x - h) + k

Front 21

What is the one-to-one property of logarithms?

Back 21

For a > 0 and a ≠ 1, if logₐ(x₁) = logₐ(x₂),
then x₁ = x₂.

Front 22

What are the steps to finding the inverse of a one-to-one function?

Back 22

1) Replace f(x) with y.
2) Interchange x and y.
3) Solve the equation for y.
4) Replace y with f⁻¹(x).
5) Check that the domain of f is the range of f⁻¹ and and that the domain of f⁻¹ is the range of f.

Front 23

What is the formula for continuous compounding?

Back 23

A = P•eʳᵗ

Front 24

Describe the graph of f(x) = aˣ

Back 24

Front 25

Describe the graph of f(x) = -aˣ

Back 25

Front 26

Describe the graph of f(x) = (1/2)ˣ

Back 26

Front 27

Describe the graph of f(x) = -(1/2)ˣ

Back 27

Front 28

Describe the graph of f(x) = log₂(x)

Back 28

Front 29

Describe the graph of f(x) = -1•log₂(x)

Back 29