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.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

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.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

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.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

Front

What does f(x) represent in function notation?

Back

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

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

Front

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

Back

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

Tags

CCSS.HSF.IF.A.2

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.

Tags

CCSS.HSF.IF.A.2

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.

Tags

CCSS.HSF-BF.B.4A

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.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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.

Tags

CCSS.8.EE.B.5