Properties of the Exponential Function

Front

What is the domain of the exponential function f(x) = a^x?

Back

The domain is the interval (-∞, ∞).

Front

What is the range of the exponential function f(x) = a^x?

Back

The range is the interval (0, ∞).

Front

What are the x-intercepts of the exponential function f(x) = a^x?

Back

There are none.

Front

What is the y-intercept of the exponential function f(x) = a^x?

Back

The y-intercept is 1.

Front

What is the horizontal asymptote of the exponential function f(x) = a^x as x approaches negative infinity?

Back

The horizontal asymptote is the x-axis (y = 0).

Front

Is the exponential function f(x) = a^x increasing or decreasing?

Back

It is increasing for a > 1 and decreasing for 0 < a < 1.

Front

What characteristics does the exponential function f(x) = a^x have?

Back

It is one-to-one, smooth, and continuous.

Front

What is the domain of the exponential function f(x) = a^x when 0 < a < 1?

Back

The domain is the interval (-∞, ∞).

Front

What is the range of the exponential function f(x) = a^x when 0 < a < 1?

Back

The range is the interval (0, ∞).

Front

Is the exponential function f(x) = a^x when 0 < a < 1 increasing or decreasing?

Back

It is decreasing.