Linear 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 table of values represents a linear function?

Back

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

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 over 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 the function when x = 0.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

Front

What is the difference between a function and a non-function?

Back

A function is a relation where each input has exactly one output, while a non-function may have an input that corresponds to multiple outputs.

Front

How can you identify a linear function from a graph?

Back

A linear function can be identified from a graph if it forms a straight line, regardless of its position on the coordinate plane.

Front

What are the characteristics of a nonlinear graph?

Back

Nonlinear graphs can curve, bend, or have varying slopes, indicating that the relationship between the variables is not constant.

Front

What is the significance of the domain and range in functions?

Back

The domain is the set of all possible input values (x-values) for a function, while the range is the set of all possible output values (y-values).