Linear or Nonlinear

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 is calculated as the change in y divided by the 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 indicates that as the x-values increase, the y-values decrease.

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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

What is the difference between linear and nonlinear equations?

Back

Linear equations represent straight lines and have a constant rate of change, while nonlinear equations represent curves and have varying rates of change.

Front

How do you graph a linear function?

Back

To graph a linear function, identify the y-intercept, plot it on the graph, and use the slope to find another point. Draw a straight line through these points.

Front

What is a quadratic function?

Back

A quadratic function is a type of nonlinear function that can be expressed in the form f(x) = ax^2 + bx + c, where a, b, and c are constants.