Final Test(RETAKE): Logarithmic Functions

Front

What is the definition of a logarithm?

Back

A logarithm is the exponent to which a base must be raised to produce a given number. For example, log_b(a) = c means b^c = a.

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power. In log_b(a), b is the base.

Front

What is the value of log_4(1)?

Back

0, because any number raised to the power of 0 equals 1.

Front

What is the value of log_5(125)?

Back

3, because 5^3 = 125.

Front

Describe the transformation of f(x) = log_9(x) to f(x) = log_9(-x + 1) - 5.

Back

Reflection about the y-axis; shift left 1 and 5 down.

Front

What is the vertical asymptote of the logarithmic function f(x) = log_b(x)?

Back

The vertical asymptote is at x = 0.

Front

What is the horizontal asymptote of the logarithmic function f(x) = log_b(x)?

Back

There is no horizontal asymptote for logarithmic functions.

Front

What is the domain of the logarithmic function f(x) = log_b(x)?

Back

The domain is x > 0.

Front

What is the range of the logarithmic function f(x) = log_b(x)?

Back

The range is all real numbers, (-∞, ∞).

Front

How does the graph of f(x) = log_b(x) behave as x approaches 0 from the right?

Back

The graph approaches negative infinity.