Identifying Linear and Nonlinear Functions

Front

What is a linear function?

Back

A linear function is a function that can be represented by a straight line on a graph. It has a constant rate of change and can be expressed in the form y = 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 be represented by equations that include exponents, roots, or other non-linear terms.

Front

How can you identify a linear function from a table of values?

Back

A linear function will have a constant difference between the y-values for equal intervals of x-values. If the differences are not constant, the function is nonlinear.

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

How can you determine if a graph represents a function?

Back

You can use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

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 does the y-intercept represent in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, representing the value of y when x is 0.

Front

Give an example of a linear function.

Back

An example of a linear function is f(x) = 2x + 3, which has a slope of 2 and a y-intercept of 3.

Front

Give an example of a nonlinear function.

Back

An example of a nonlinear function is f(x) = x^2, which forms a parabola when graphed.

Front

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

Back

A linear equation can be written in the form y = mx + b, while a nonlinear equation cannot be expressed in this form and may include variables raised to powers other than one.