Transformations of Exponential Functions (4A)

Front

What is an asymptote?

Back

An imaginary horizontal line that helps define where the graph will approach, but never reach.

Front

Back

(0, 4)

Front

What is the x-intercept of the exponential function?

Back

There is not one.

Front

What does the notation x → -∞ represent?

Back

It means the graph is moving to the left.

Front

What does the notation x → ∞ represent?

Back

It means the graph is moving to the right.

Front

What is the formula for compound interest?

Back

A = P(1 + r/n)^(nt) where A is the amount, P is the principal, r is the rate, n is the number of times interest is compounded per year, and t is the time in years.

Front

If a function has a horizontal asymptote at y = 3, what does this mean?

Back

As x approaches infinity, the function approaches the value of 3.

Front

What is the general form of an exponential function?

Back

y = ab^x, where a is a constant and b is the base.

Front

What happens to the graph of an exponential function as x approaches negative infinity?

Back

The graph approaches the horizontal asymptote, typically y = 0.

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.