Identifying 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 identify a linear function from a table of values?

Back

A linear function will have a constant rate of change between the x-values and y-values. If the differences in y-values divided by the differences in x-values are the same, the function is linear.

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of its steepness, represented by 'm' in the equation f(x) = mx + b. It indicates how much y changes for a unit change in x.

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. It is represented by 'b' in the equation f(x) = mx + b.

Front

Can a linear function have a negative slope?

Back

Yes, a linear function can have a negative slope, which means that as x increases, y decreases.

Front

What is an example of a nonlinear function?

Back

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

Front

How do you determine if a function is linear or nonlinear from a graph?

Back

If the graph is a straight line, the function is linear. If the graph curves or has any bends, the function is nonlinear.

Front

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

Back

A linear equation can be written in the form Ax + By = C, where A, B, and C are constants. A nonlinear equation cannot be expressed in this form and may include variables raised to a power greater than one.

Front

What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions for different intervals of the input variable.