Attributes of Exponential Functions Practice

Front

What is the domain of an exponential function?

Back

The domain of an exponential function is all real numbers, expressed as: $$-\infty < x < \infty$$.

Front

What is the y-intercept of an exponential function?

Back

The y-intercept of an exponential function is the point where the graph crosses the y-axis, typically at (0, a) where a is the initial value.

Front

What does it mean if an exponential function represents growth?

Back

An exponential function represents growth if the base of the exponent is greater than 1, indicating that the function increases as x increases.

Front

What does it mean if an exponential function represents decay?

Back

An exponential function represents decay if the base of the exponent is between 0 and 1, indicating that the function decreases as x increases.

Front

What is a horizontal asymptote in the context of exponential functions?

Back

A horizontal asymptote is a horizontal line that the graph of the function approaches as x approaches infinity or negative infinity.

Front

How do you find the horizontal asymptote of an exponential function?

Back

The horizontal asymptote of an exponential function of the form $$y = a \cdot b^{x} + c$$ is given by the value of c as x approaches infinity.

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is $$y = a \cdot b^{x}$$ where a is a constant, b is the base (b > 0), and x is the exponent.

Front

What is the significance of the base in an exponential function?

Back

The base determines the rate of growth or decay: if b > 1, the function grows; if 0 < b < 1, the function decays.

Front

What is the range of an exponential function?

Back

The range of an exponential function is all positive real numbers, expressed as: $$0 < y < \infty$$.

Front

How do you determine if an exponential function is increasing or decreasing?

Back

An exponential function is increasing if the base is greater than 1 and decreasing if the base is between 0 and 1.