Exponential and Logarithmic Functions

Front

What is the definition of an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is a positive real number, and x is the exponent.

Front

What is the definition of a logarithmic function?

Back

A logarithmic function is the inverse of an exponential function, expressed as f(x) = log_b(x), which answers the question: 'To what exponent must b be raised, to produce x?'

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number b in the expression log_b(x), which indicates the number that is raised to a power to obtain x.

Tags

CCSS.HSF.BF.B.5

Front

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

Back

The vertical asymptote of the function f(x)=log_b(x) is x = 0.

Tags

CCSS.HSF-IF.C.7E

Front

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

Back

The function f(x)=log_b(x) does not have a horizontal asymptote.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find the domain of a logarithmic function?

Back

The domain of a logarithmic function f(x) = log_b(x) is x > 0.

Front

How do you find the range of a logarithmic function?

Back

The range of a logarithmic function f(x) = log_b(x) is all real numbers (-∞, ∞).

Front

What transformation occurs in the function f(x)=log_b(x-h)+k?

Back

The function is translated h units to the right and k units up.

Front

What is the effect of a negative coefficient in front of a logarithmic function?

Back

A negative coefficient reflects the graph of the logarithmic function across the x-axis.

Tags

CCSS.HSF-IF.C.7E

Front

What is the relationship between exponential and logarithmic functions?

Back

Exponential functions and logarithmic functions are inverses of each other; if y = b^x, then x = log_b(y).

Tags

CCSS.HSF.BF.B.5