Extended LSAE-Exponential Functions for 3/28/25

Front

What is the domain of an exponential function?

Back

The domain of an exponential function is all real numbers, typically expressed as (-∞, ∞).

Front

What is the general form of an exponential function?

Back

The general form is y = a(b^x), where a is a constant, b is the base, and x is the exponent.

Front

What does it mean for a function to exhibit exponential growth?

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, typically represented by a function of the form y = a(b^x) where b > 1.

Front

What does it mean for a function to exhibit exponential decay?

Back

Exponential decay occurs when the value decreases at a rate proportional to its current value, typically represented by a function of the form y = a(b^x) where 0 < b < 1.

Front

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

Back

The y-intercept is found by evaluating the function at x = 0, which gives y = a(b^0) = a.

Front

What is the range of an exponential function?

Back

The range of an exponential function is (0, ∞) for growth and (0, a) for decay, where a is the initial value.

Front

What is the significance of the base in an exponential function?

Back

The base determines the rate of growth or decay; if b > 1, the function grows, and if 0 < b < 1, the function decays.

Front

How can you identify an exponential function from a table of values?

Back

An exponential function will show a constant ratio between consecutive y-values when x-values are equally spaced.

Front

What is the formula for calculating the growth factor in an exponential function?

Back

The growth factor is represented by the base b in the function y = a(b^x).

Front

What is the difference between linear and exponential functions?

Back

Linear functions have a constant rate of change, while exponential functions have a rate of change that increases or decreases exponentially.