Linear vs Nonlinear Functions

Front

What is 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.

Front

What is 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.

Front

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

Back

A function is linear if the differences between consecutive y-values divided by the differences between consecutive x-values are constant.

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output (y-value) for each input (x-value).

Front

What does it mean for a relation to not be a function?

Back

A relation is not a function if at least one x-value is associated with more than one y-value.

Front

What is the slope of a linear function?

Back

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

Front

What is the y-intercept of a linear function?

Back

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

Front

How can you identify a nonlinear function from its graph?

Back

A nonlinear function can be identified by its curved graph, which does not form a straight line.

Front

What is a common example of a nonlinear function?

Back

A common example of a nonlinear function is a quadratic function, which can be represented by the equation f(x) = ax^2 + bx + c.

Front

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

Back

A linear equation is an equation that represents a straight line, while a linear function is a specific type of linear equation that defines a relationship between x and y.