Exponential Functions Key Features

Front

What is an exponential function?

Back

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 exponent.

Front

What is the y-intercept of an exponential function?

Back

The point where the graph of the function crosses the y-axis, found by evaluating f(0).

Front

What is the x-intercept of an exponential function?

Back

Exponential functions do not have an x-intercept; they never cross the x-axis.

Front

What does it mean if an exponential function is increasing?

Back

The function is growing, meaning as x increases, f(x) also increases.

Front

What does it mean if an exponential function is decreasing?

Back

The function is shrinking, meaning as x increases, f(x) decreases.

Front

What is the initial value in an exponential function?

Back

The value of the function when x = 0, represented by 'a' in f(x) = a * b^x.

Front

What is the base of an exponential function?

Back

The constant 'b' in the function f(x) = a * b^x, which determines the growth or decay rate.

Front

What is exponential growth?

Back

A situation where the function increases rapidly as x increases, typically when b > 1.

Front

What is exponential decay?

Back

A situation where the function decreases rapidly as x increases, typically when 0 < b < 1.

Front

How do you find the y-intercept of f(x) = 300(1.16)^x?

Back

Evaluate f(0): f(0) = 300(1.16)^0 = 300.