Exponential Function Flashcard

Front

What is the domain of the exponential function?

Back

All real numbers.

Front

What is the initial value of a population of fish that starts at 8,000 and decreases by 6% per year?

Back

8,000.

Front

Identify the common ratio (multiplier) of the function f(x)=2(4)^x.

Back

4.

Front

What is the average rate of change of the function from x=-1 to x=0 if f(-1) = 2 and f(0) = 0?

Back

-2.

Front

What is the range of the exponential function?

Back

y > -2.

Front

Define an exponential function.

Back

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

Front

What does the base of an exponential function represent?

Back

The base indicates the growth (b > 1) or decay (0 < b < 1) rate of the function.

Front

How does an exponential function behave as x approaches infinity?

Back

It increases without bound if b > 1 or approaches 0 if 0 < b < 1.

Front

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

Back

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

Front

What is the effect of changing the base in an exponential function?

Back

Changing the base affects the rate of growth or decay of the function.