Is it a Function? & Describe Graphs

Front

What is a function?

Back

A function is a relation where each input (x-value) has exactly one output (y-value).

Front

Which of the following sets is not a function? (3,4) (4,-3) (7,4) (3,8)

Back

This set is not a function because the input '3' corresponds to two different outputs (4 and 8).

Front

What does it mean for a graph to slowly decrease at a constant rate?

Back

It means that as the x-values increase, the y-values decrease steadily without changing the rate of decrease.

Front

How can you tell if a relation is a function from a graph?

Back

Use the vertical line test: if a vertical line crosses the graph more than once, it is not a function.

Front

What does it mean when a graph stays the same?

Back

It means that the y-value does not change as the x-value changes; the graph is horizontal.

Front

What happens in a graph when the object is slowing down?

Back

The slope of the graph decreases, indicating that the rate of change of the y-value is lessening.

Front

What is the definition of a linear function?

Back

A linear function is a function that graphs to a straight line, represented by the equation y = mx + b.

Front

What is the slope of a line?

Back

The slope is a measure of the steepness of a line, calculated as the change in y divided by the change in x (rise/run).

Front

What does a positive slope indicate about a function?

Back

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

Front

What does a negative slope indicate about a function?

Back

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