Linear v. 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 identify a linear function from its equation?

Back

A linear function can be identified by its equation in the form y = mx + b, where m and b are constants. If the equation includes variables multiplied together or raised to a power other than one, it is nonlinear.

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 y = 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 y = mx + b.

Front

Give an example of a linear function.

Back

An example of a linear function is f(x) = 2x + 3. This function 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 + 2. This function forms a parabola when graphed.

Front

What is the difference between the graphs of linear and nonlinear functions?

Back

The graph of a linear function is a straight line, while the graph of a nonlinear function can be curved or take various shapes depending on the function type.

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 and a ≠ 0.

Front

What is an exponential function?

Back

An exponential function is a nonlinear function of the form f(x) = a * b^x, where a is a constant, b is the base, and x is the exponent.