Identify Function Characteristics

Front

What is a constant function?

Back

A constant function is a function that does not change its value regardless of the input. It is represented as f(x) = c, where c is a constant.

Front

What does it mean for a function to be linear?

Back

A function is linear if it can be graphically represented as a straight line. This means that the change in y is proportional to the change in x, resulting in a constant rate of change.

Tags

CCSS.8.F.A.3

Front

What is the definition of a discrete function?

Back

A discrete function is a function that has distinct, separate values. It is not continuous and is often represented by a set of individual points.

Front

What is the definition of a continuous function?

Back

A continuous function is a function that does not have any breaks, jumps, or holes in its graph. It can be drawn without lifting the pencil from the paper.

Front

How do you determine the interval where a function is increasing?

Back

A function is increasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2 then f(x1) < f(x2).

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x-value) is associated with exactly one output (y-value). A relation can have multiple outputs for a single input.

Tags

CCSS.8.F.A.1

Front

What is the significance of the interval notation 3 < x < 5?

Back

The interval notation 3 < x < 5 indicates that x can take any value between 3 and 5, but not including 3 and 5 themselves.

Front

What does it mean for a function to be nonlinear?

Back

A nonlinear function is one that does not form a straight line when graphed. This means the rate of change is not constant.

Tags

CCSS.8.F.A.3

Front

What is the role of the x and y coordinates in determining linearity?

Back

In a linear function, the x and y coordinates change at a constant rate, meaning the ratio of the change in y to the change in x remains the same.

Tags

CCSS.HSF-LE.A.1B

Front

What is an example of a function that is not a function?

Back

An example of a relation that is not a function is the set of points {(1,2), (1,3)}, where the input 1 corresponds to two different outputs.

Tags

CCSS.8.F.A.1