Exponential Graphs

Front

What is the y-intercept of an exponential function?

Back

The y-intercept is the point where the graph crosses the y-axis, represented as (0, f(0)). For example, in the function y = 2^x, the y-intercept is (0, 1).

Front

What is an asymptote in the context of exponential graphs?

Back

An asymptote is a line that the graph approaches but never touches. For example, the horizontal asymptote of the function y = 2^x is y = 0.

Front

What does it mean for a function to exhibit exponential growth?

Back

Exponential growth occurs when a function increases rapidly as the input increases. For example, y = 2^x shows exponential growth.

Front

What does it mean for a function to exhibit exponential decay?

Back

Exponential decay occurs when a function decreases rapidly as the input increases. For example, y = (1/2)^x shows exponential decay.

Front

How do you identify the y-intercept from a graph?

Back

The y-intercept can be identified as the point where the graph intersects the y-axis, which occurs when x = 0.

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is y = a * b^x, where 'a' is a constant, 'b' is the base, and 'x' is the exponent.

Front

What is the base in an exponential function?

Back

The base is the constant 'b' in the function y = a * b^x, which determines the rate of growth or decay.

Front

What happens to the graph of y = 2^x as x approaches negative infinity?

Back

As x approaches negative infinity, the graph approaches the horizontal asymptote y = 0.

Front

What is the significance of the point (0,1) in exponential functions?

Back

The point (0,1) represents the y-intercept of the function y = b^x when b > 0, indicating the value of the function at x = 0.

Front

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

Back

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