Finding Function Rules

Front

What is a function rule?

Back

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

Front

How do you write a function rule for a situation involving cost?

Back

To write a function rule for cost, identify the cost per unit and multiply it by the number of units. For example, if the cost is $35 per hour, the function rule is c = 35h.

Front

What is the output of the function rule x + 9 when x = 5?

Back

The output is 14, calculated as 5 + 9.

Front

How do you determine the function rule from a table of values?

Back

To determine the function rule from a table, identify the pattern in the input-output pairs and express it as an equation.

Front

What is the function rule for the sequence {(1,4), (2,8), (3,12), (4,16)}?

Back

The function rule is 4x, where x is the input.

Front

What does the slope represent in a linear function?

Back

The slope represents the rate of change of the output value with respect to the input value.

Front

What is the y-intercept in a linear function?

Back

The y-intercept is the value of the output when the input is zero, represented as the constant term in the function rule.

Front

How can you identify a linear function from a set of points?

Back

A linear function can be identified if the points form a straight line when plotted on a graph.

Front

What is the general form of a linear function?

Back

The general form of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the function rule for a given input-output pair?

Back

To find the function rule, analyze the relationship between the input and output values and express it as an equation.