Identifying Characteristics Exponential Graphs

Front

What is an asymptote in the context of exponential graphs?

Back

An asymptote is a line that a graph approaches but never touches. For exponential functions, the horizontal asymptote is typically y=0.

Front

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

Back

Exponential growth occurs when a quantity increases at a rate proportional to its current value, resulting in a rapid increase over time.

Front

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

Back

Exponential decay occurs when a quantity decreases at a rate proportional to its current value, leading to a rapid decrease over time.

Front

What is the initial value in an exponential function?

Back

The initial value is the value of the function when the independent variable (usually x) is zero.

Front

How can you identify if a graph represents exponential growth or decay?

Back

If the graph rises as it moves from left to right, it represents exponential growth. If it falls, it represents exponential decay.

Front

What is the general form of an exponential function?

Back

The general form is f(x) = a * b^x, where 'a' is the initial value and 'b' is the growth (b > 1) or decay (0 < b < 1) factor.

Front

What does the base 'b' represent in an exponential function?

Back

The base 'b' indicates the growth or decay factor. If b > 1, the function grows; if 0 < b < 1, the function decays.

Front

What is the significance of the y-intercept in an exponential graph?

Back

The y-intercept represents the initial value of the function, which is the point where the graph crosses the y-axis.

Front

How do you determine the rate of growth or decay in an exponential function?

Back

The rate of growth or decay can be determined by the base 'b' in the function f(x) = a * b^x. A larger base indicates faster growth.

Front

What is the effect of changing the initial value 'a' in an exponential function?

Back

Changing the initial value 'a' shifts the graph vertically. A larger 'a' results in a higher starting point on the y-axis.