logarithmic and exponential inverses and graphs

Front

What is the inverse of an exponential function?

Back

A logarithmic function.

Front

True or False: The inverse of an exponential function is its reflection across the x-axis.

Back

False. The inverse is a reflection across the line y=x.

Front

What is the horizontal asymptote of the function f(x) = 3(2)^(x-4) + 5?

Back

y = 5.

Front

What is the general form of an exponential function?

Back

f(x) = a * b^x, where a is a constant and b is the base.

Front

What is the general form of a logarithmic function?

Back

f(x) = log_b(x), where b is the base.

Front

How do you convert an exponential equation to logarithmic form?

Back

If b^y = x, then log_b(x) = y.

Front

What is the base of the natural logarithm?

Back

e (approximately 2.718).

Front

What is the relationship between logarithmic and exponential functions?

Back

They are inverses of each other.

Front

What is the domain of a logarithmic function?

Back

The domain is (0, ∞).

Front

What is the range of an exponential function?

Back

The range is (0, ∞) for a base greater than 1.