Function Machines

Front

What is a function machine?

Back

A function machine is a conceptual tool used to describe a process that takes an input, applies a specific rule or function, and produces an output.

Front

Define input in the context of function machines.

Back

Input is the value or number that is fed into a function machine to be processed.

Front

Define output in the context of function machines.

Back

Output is the result or value produced by a function machine after processing the input.

Front

What does f(x) represent in function notation?

Back

f(x) represents the output of a function f when the input is x.

Front

If f(x) = 2x + 3, what is f(2)?

Back

f(2) = 2(2) + 3 = 7.

Front

How do you find the output of a function machine?

Back

To find the output, substitute the input value into the function's rule and calculate the result.

Front

What is the inverse of a function?

Back

The inverse of a function reverses the roles of input and output, allowing you to find the original input from a given output.

Front

If the output is 10 and the function is f(x) = x + 5, what is the input?

Back

To find the input, set the equation: 10 = x + 5. Thus, x = 5.

Front

What is a linear function?

Back

A linear function is a function that creates a straight line when graphed, typically in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is the slope in a linear function?

Back

The slope (m) indicates the steepness of the line and the direction it goes; a positive slope rises, while a negative slope falls.