Identifying Characteristics Exponential Graphs

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 the base (a positive real number), and 'x' is the exponent.

Front

What is the characteristic of exponential growth?

Back

In exponential growth, the function increases rapidly as 'x' increases, and the base 'b' is greater than 1.

Front

What is the characteristic of exponential decay?

Back

In exponential decay, the function decreases rapidly as 'x' increases, and the base 'b' is between 0 and 1.

Front

What does the term 'asymptote' refer to in exponential graphs?

Back

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

Front

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

Back

An exponential growth function will show a curve that rises steeply to the right, indicating rapid increase.

Front

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

Back

An exponential decay function will show a curve that falls steeply to the right, indicating rapid decrease.

Front

What is the value of f(1) in the exponential function f(x) = 3^x?

Back

f(1) = 3.

Front

What is the value of f(0) in any exponential function?

Back

f(0) = a, where 'a' is the initial value of the function.

Front

What happens to the value of an exponential decay function as x approaches infinity?

Back

As x approaches infinity, the value of an exponential decay function approaches 0.

Front

What happens to the value of an exponential growth function as x approaches infinity?

Back

As x approaches infinity, the value of an exponential growth function approaches infinity.