Basic Function Rules

Front

What is a function rule?

Back

A function rule is a mathematical expression that describes the relationship between input (x) and output (y) values in a function.

Front

What does the notation y = mx + b represent?

Back

This notation represents the equation of a linear function, where m is the slope and b is the y-intercept.

Front

How do you find the output of a function given an input?

Back

To find the output, substitute the input value into the function rule and simplify.

Front

What is the slope in a linear function?

Back

The slope (m) indicates how steep the line is and the direction it goes; it represents the rate of change of y with respect to x.

Front

What is the y-intercept in a linear function?

Back

The y-intercept (b) is the point where the line crosses the y-axis, representing the output when the input (x) is 0.

Front

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

Back

f(2) = 2(2) + 3 = 4 + 3 = 7.

Front

What is the function rule for the table: (1, 6), (2, 8), (3, 10)?

Back

The function rule is y = 2x + 4.

Front

If my function rule is 3x + 2 and my OUTPUT is 11, what is my input?

Back

To find the input, set 3x + 2 = 11. Solving gives x = 3.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input has exactly one output.

Front

What does it mean for a function to be linear?

Back

A linear function creates a straight line when graphed and has a constant rate of change.