Identifying Functions: Maps and Tables

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What does it mean for a table to represent a function?

Back

A table represents a function if each input (x-value) corresponds to exactly one output (y-value).

Front

What is a positive slope?

Back

A positive slope indicates that as the x-values increase, the y-values also increase.

Front

What is a negative slope?

Back

A negative slope indicates that as the x-values increase, the y-values decrease.

Front

What does an undefined slope indicate?

Back

An undefined slope occurs in vertical lines where the x-value does not change, leading to division by zero.

Front

What does a zero slope indicate?

Back

A zero slope indicates a horizontal line where the y-value remains constant as the x-value changes.

Front

How do you determine if a table is a function?

Back

Check if any x-value is repeated with different y-values; if so, it is not a function.

Front

What is the slope formula?

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What is the slope of the line through the points (2, 3) and (4, 7)?

Back

The slope is m = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

What is the slope of the line through the points (1, 2) and (1, 5)?

Back

The slope is undefined because the x-values are the same, leading to division by zero.