Exponential functions

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 does the base 'b' in an exponential function represent?

Back

The base 'b' represents the growth (if b > 1) or decay (if 0 < b < 1) factor of the function.

Front

What is the general shape of the graph of an exponential function?

Back

The graph of an exponential function is a curve that increases rapidly (for b > 1) or decreases rapidly (for 0 < b < 1) as x moves away from the y-axis.

Front

What is the y-intercept of an exponential function?

Back

The y-intercept of an exponential function f(x) = a * b^x is the point (0, a).

Front

What is the domain of an exponential function?

Back

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

Front

What is the range of an exponential function?

Back

The range of an exponential function is all positive real numbers, (0, ∞).

Front

How do you determine if a function is exponential?

Back

A function is exponential if it can be expressed in the form f(x) = a * b^x, where 'a' is a constant and 'b' is a positive real number.

Front

What is the x-intercept of an exponential function?

Back

An exponential function does not have an x-intercept; it never crosses the x-axis.

Front

What is the common ratio in a geometric sequence?

Back

The common ratio is the factor by which each term of a geometric sequence is multiplied to get the next term.

Front

If the common ratio is 1/2, what does this indicate about the sequence?

Back

If the common ratio is 1/2, the sequence is decreasing, as each term is half of the previous term.