13.1 and 13.2 Practice

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 variable. It shows rapid growth or decay.

Front

What is the general form of an exponential decay function?

Back

An exponential decay function can be expressed as f(x) = a * e^(-bx), where a > 0, b > 0, and e is the base of the natural logarithm.

Front

What does the graph of an exponential growth function look like?

Back

The graph of an exponential growth function rises steeply as x increases, approaching infinity as x approaches positive infinity.

Front

What does the graph of an exponential decay function look like?

Back

The graph of an exponential decay function decreases rapidly and approaches zero as x increases.

Front

What is the end behavior of the function y = 4^x + 3?

Back

As x → ∞, y → ∞ and as x → -∞, y → 3.

Front

What is the domain of the function y = 4^x + 3?

Back

The domain is all real numbers, (-∞, ∞).

Front

What is the range of the function y = 4^x + 3?

Back

The range is (3, ∞) because the function approaches 3 but never reaches it.

Front

What is an asymptote?

Back

An asymptote is a line that a graph approaches but never touches. For exponential functions, the horizontal asymptote is often y = 0.

Front

What is the horizontal asymptote of the function y = 2^(x-3)?

Back

The horizontal asymptote is y = 0.

Front

What is the vertical asymptote of the function y = 2^(x-3)?

Back

There is no vertical asymptote for this function.