Find the Rule of a Function

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

How do you represent a linear function?

Back

A linear function can be represented in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a function represent?

Back

The slope represents the rate of change of the function; it indicates how much the output (y) changes for a unit change in the input (x).

Front

What is the y-intercept in a function?

Back

The y-intercept is the value of y when x is 0; it represents the point where the graph of the function crosses the y-axis.

Front

If a function is defined as y = 3x + 1, what is the output when x = 2?

Back

When x = 2, y = 3(2) + 1 = 7.

Front

What does it mean if a function is increasing?

Back

A function is increasing if, as the input (x) increases, the output (y) also increases.

Front

What does it mean if a function is decreasing?

Back

A function is decreasing if, as the input (x) increases, the output (y) decreases.

Front

How can you determine if a function is linear from a table of values?

Back

A function is linear if the differences between consecutive y-values are constant for equal differences in x-values.

Front

What is the function rule for a situation where the output is eight more than the input?

Back

The function rule is y = x + 8.

Front

How do you find the function rule from a word problem?

Back

Identify the quantities involved, determine how they relate to each other, and express this relationship mathematically.