Flashcard - Exponentials and Comparing Functions

Front

What is an Exponential Function?

Back

A function of the form f(x) = a * b^x, where a is a constant, b is a positive real number, and b ≠ 1.

Front

What is a Linear Function?

Back

A function that can be graphically represented in the Cartesian plane as a straight line, typically in the form f(x) = mx + b.

Front

What is a Quadratic Function?

Back

A function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the growth factor in an exponential function?

Back

The base 'b' in the function f(x) = a * b^x, where b > 1 indicates growth.

Front

What is the decay factor in an exponential function?

Back

The base 'b' in the function f(x) = a * b^x, where 0 < b < 1 indicates decay.

Front

How do you identify an Exponential Decay function?

Back

If the function is in the form f(x) = a * b^x with 0 < b < 1, it represents exponential decay.

Front

How do you identify an Exponential Growth function?

Back

If the function is in the form f(x) = a * b^x with b > 1, it represents exponential growth.

Front

What is the general form of a function?

Back

A mathematical expression that describes a relationship between variables, typically written as f(x) = expression.

Front

What does it mean for a function to be 'not a function'?

Back

A relation where each input does not have exactly one output, such as a vertical line test failing.

Front

What is the significance of the coefficient 'a' in an exponential function?

Back

It represents the initial value or the y-intercept of the function when x = 0.