Exponential Functions - PCM Unit 6A

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 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

How can you identify an exponential growth function from its graph?

Back

An exponential growth function's graph rises steeply to the right, showing that as 'x' increases, 'f(x)' increases rapidly.

Front

How can you identify an exponential decay function from its graph?

Back

An exponential decay function's graph falls steeply to the right, indicating that as 'x' increases, 'f(x)' decreases rapidly.

Front

What is the base 'b' in an exponential function?

Back

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

Front

What is the y-intercept of an exponential function?

Back

The y-intercept of an exponential function is the value of f(x) when x = 0, which is equal to 'a' in the function f(x) = a * b^x.

Front

What is the horizontal asymptote of an exponential decay function?

Back

The horizontal asymptote of an exponential decay function is the line y = 0, which the graph approaches but never touches as x increases.

Front

What is the difference between linear and exponential functions?

Back

Linear functions increase or decrease by a constant amount, while exponential functions increase or decrease by a constant percentage.

Front

Can exponential functions have negative values?

Back

Exponential functions of the form f(x) = a * b^x, where a > 0, will always yield positive values for all real x.