Review: Properties of Exponential Function

Front

What is the definition of an asymptote in the context of exponential functions?

Back

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

Front

What is the horizontal asymptote of the function y = 2^x - 3?

Back

The horizontal asymptote is y = -3.

Front

What is the range of the exponential function y = 3(2^(x-7))?

Back

The range is R: (0, ∞).

Front

How do you determine the y-intercept of an exponential function?

Back

To find the y-intercept, evaluate the function at x = 0.

Front

What is the y-intercept of the function y = 3^x?

Back

The y-intercept is (0, 1).

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is y = a * b^(x - h) + k, where (h, k) is the translation of the graph.

Front

What does the base of an exponential function indicate?

Back

The base indicates the growth or decay rate of the function. 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 the effect of changing the value of 'k' in the function y = a * b^x + k?

Back

Changing 'k' vertically shifts the graph up or down. If k is positive, the graph shifts up; if k is negative, it shifts down.

Front

What is the significance of the value 'a' in the exponential function y = a * b^x?

Back

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

Front

How does the transformation y = a * b^(x - h) + k affect the graph of y = b^x?

Back

The transformation shifts the graph horizontally by 'h' units and vertically by 'k' units.