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 is the general form of an exponential function?

Back

The general form of an exponential function is f(x) = a * b^x, where 'a' is the initial value and 'b' is the growth (b > 1) or decay (0 < b < 1) factor.

Front

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

Back

The base 'b' in an exponential function represents the growth or decay factor. If b > 1, the function represents exponential growth; if 0 < b < 1, it represents exponential decay.

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 value of f(0), which equals 'a'.

Front

How do you evaluate an exponential function at a specific point?

Back

To evaluate an exponential function at a specific point, substitute the value of 'x' into the function and calculate the result.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base 'b' is greater than 1, leading to an increase in value as 'x' increases. Exponential decay occurs when the base 'b' is between 0 and 1, leading to a decrease in value as 'x' increases.

Front

What is the initial value in the function f(x) = 5 * 3^x?

Back

The initial value in the function f(x) = 5 * 3^x is 5.

Front

How do you find the y-intercept of the function f(x) = 2 * 4^x?

Back

To find the y-intercept of f(x) = 2 * 4^x, evaluate f(0): f(0) = 2 * 4^0 = 2 * 1 = 2.

Front

What is the value of f(1) for the function f(x) = 10 * 2^x?

Back

f(1) = 10 * 2^1 = 10 * 2 = 20.

Front

What does it mean for a graph to be a function?

Back

A graph is a function if every x-value has exactly one corresponding y-value, which can be tested using the vertical line test.