Exponential Functions

Front

What is an exponential function?

Back

An exponential function is 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 does the base 'b' in an exponential function represent?

Back

The base 'b' determines the rate of growth or decay of the function. If b > 1, the function represents exponential growth; if 0 < b < 1, it represents exponential decay.

Front

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

Back

The y-intercept is the value of the function when x = 0, which is f(0) = a.

Front

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

Back

The graph of an increasing exponential function rises steeply from left to right, starting from the y-intercept.

Front

What is the range of an exponential function?

Back

The range of an exponential function is all real numbers greater than 0.

Front

What is the domain of an exponential function?

Back

The domain of an exponential function is all real numbers.

Front

What type of function is y = 3(2)^x?

Back

Exponential Growth.

Front

What type of function is y = 4(0.5)^x?

Back

Exponential Decay.

Front

How do you identify an exponential growth function?

Back

An exponential growth function has a base greater than 1.

Front

How do you identify an exponential decay function?

Back

An exponential decay function has a base between 0 and 1.