Graphs of Exponential Functions

Front

What is an exponential function?

Back

A mathematical function of the form f(x) = a * b^x, where a is a constant, b is a positive real number, and x is the exponent.

Front

What is the general shape of the graph of an exponential growth function?

Back

The graph rises rapidly to the right and approaches the x-axis but never touches it.

Front

What is the general shape of the graph of an exponential decay function?

Back

The graph falls rapidly to the right and approaches the x-axis but never touches it.

Front

What is a transformation in the context of graphs?

Back

A change made to the graph of a function, such as shifting, reflecting, stretching, or compressing.

Front

What does it mean for a function to have a horizontal asymptote?

Back

A horizontal line that the graph of the function approaches as x approaches positive or negative infinity.

Front

What is the range of the function f(x) = a * b^x for a > 0 and b > 1?

Back

The range is (0, ∞).

Front

What is the range of the function f(x) = a * b^x for a < 0 and b > 1?

Back

The range is (-∞, 0).

Front

What is the y-intercept of an exponential function f(x) = a * b^x?

Back

The y-intercept is the value of f(0), which equals a.

Front

How do you evaluate an exponential function?

Back

Substitute the value of x into the function and calculate the result.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base b > 1, while exponential decay occurs when the base 0 < b < 1.