Exponential Functions (Graphs)

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 (a positive real number), and 'x' is the exponent.

Front

What does the base of an exponential function determine?

Back

The base of an exponential function determines the rate of growth or decay. If the base is greater than 1, the function represents exponential growth; if the base is between 0 and 1, it represents exponential decay.

Front

What is an asymptote in the context of exponential functions?

Back

An asymptote is a line that a graph approaches but never touches. For exponential functions, the horizontal asymptote is typically the value that the function approaches as x approaches infinity or negative infinity.

Front

What is the horizontal asymptote of the function y = (1/2)^x + 2?

Back

The horizontal asymptote of the function y = (1/2)^x + 2 is y = 2.

Front

How can you identify exponential growth on a graph?

Back

Exponential growth can be identified on a graph by a curve that rises steeply as x increases, indicating that the function's value increases rapidly.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base of the exponential function is greater than 1, leading to an increase in value. Exponential decay occurs when the base is between 0 and 1, leading to a decrease in value.

Front

What is the y-intercept of the exponential function y = 3(2)^x?

Back

The y-intercept of the function y = 3(2)^x is 3, which occurs when x = 0.

Front

How do you find the equation of an exponential function from a graph?

Back

To find the equation of an exponential function from a graph, identify the y-intercept and the base by observing the growth or decay rate, then use the general form y = a(b)^x.

Front

What is the significance of the constant 'a' in the exponential function y = a(b)^x?

Back

The constant 'a' represents the initial value or the y-intercept of the exponential function when x = 0.

Front

What does it mean if an exponential function has a horizontal asymptote at y = k?

Back

If an exponential function has a horizontal asymptote at y = k, it means that as x approaches infinity or negative infinity, the function's value approaches k but never actually reaches it.