linear vs. nonlinear

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 f(x) = 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 the definition of a nonlinear function?

Back

A nonlinear function is a function that does not form a straight line when graphed. Its rate of change is not constant, and it can take various forms such as quadratic, exponential, or logarithmic.

Tags

CCSS.8.F.A.3

Front

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

Back

To determine if a function is linear from a table, check if the ratio of the change in y to the change in x (the slope) is constant for all intervals. If it is constant, the function is linear; if not, it is nonlinear.

Tags

CCSS.8.F.A.3

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of the steepness of the line, calculated as the change in y divided by the change in x (rise/run). It indicates how much y changes for a unit change in x.

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept of a linear function?

Back

The y-intercept of a linear function is the point where the line crosses the y-axis, represented by the value of b in the equation f(x) = mx + b.

Front

What are some common forms of nonlinear functions?

Back

Common forms of nonlinear functions include quadratic functions (e.g., f(x) = ax^2 + bx + c), exponential functions (e.g., f(x) = a * b^x), and logarithmic functions (e.g., f(x) = log_b(x)).

Front

What is the graphical representation of a linear function?

Back

The graphical representation of a linear function is a straight line that can extend infinitely in both directions.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is the graphical representation of a nonlinear function?

Back

The graphical representation of a nonlinear function can take various shapes, such as curves, parabolas, or other non-straight line forms.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

Front

How do you identify a linear equation from a set of equations?

Back

To identify a linear equation, look for equations that can be expressed in the form y = mx + b, where m and b are constants. Nonlinear equations will include variables raised to powers other than one or involve products of variables.

Tags

CCSS.8.F.A.3

Front

What is the significance of the constant rate of change in linear functions?

Back

The constant rate of change in linear functions means that for every unit increase in x, the change in y is always the same, indicating a direct proportionality between x and y.

Tags

CCSS.HSF-LE.A.1B