Functions, Linearity, and Qualitative Graphs

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. In other words, for every x-value, there is one and only one y-value.

Tags

CCSS.8.F.A.1

Front

What is the definition of a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not form a straight line when graphed. Its output does not change at a constant rate.

Tags

CCSS.8.F.A.3

Front

How can you determine if a mapping is a function?

Back

A mapping is a function if each input (x-value) corresponds to exactly one output (y-value). If any input has more than one output, it is not a function.

Tags

CCSS.8.F.A.1

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, as the x-values increase, the y-values also increase.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, as the x-values increase, the y-values decrease.

Front

What is a constant function?

Back

A constant function is a function that does not change its value; it remains the same for all inputs. Its graph is a horizontal line.

Front

What is the difference between a linear function and a nonlinear function?

Back

A linear function has a constant rate of change and graphs as a straight line, while a nonlinear function has a variable rate of change and graphs as a curve.

Tags

CCSS.8.F.A.3

Front

What is the significance of the slope in a linear function?

Back

The slope (m) indicates the steepness of the line and the direction of the relationship between x and y. A positive slope means the function is increasing, while a negative slope means it is decreasing.

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept in a linear function?

Back

The y-intercept (b) is the point where the line crosses the y-axis, representing the value of y when x is 0.