Identifying Linear and 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 f(x) = mx + b. If the highest exponent of the variable is 1, it is linear.

Front

What is the significance of the slope in a linear function?

Back

The slope (m) in a linear function represents the rate of change of the function. It indicates how much the output (y) changes for a unit change in the input (x).

Front

What does the y-intercept represent in a linear function?

Back

The y-intercept (b) is the point where the graph of the function crosses the y-axis. It represents the value of the function when x = 0.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

How do you determine if a function is linear or nonlinear from a table of values?

Back

To determine if a function is linear or nonlinear from a table of values, check if the differences between consecutive y-values are constant. If they are constant, the function is linear; if not, it is nonlinear.

Front

What is the output of the function f(x) = x^2 - 5x when x = 4?

Back

The output is f(4) = 4^2 - 5(4) = 16 - 20 = -4.

Front

What is the output of the function f(x) = x + 3 when x = -5?

Back

The output is f(-5) = -5 + 3 = -2.

Front

What does it mean for a function to have a constant rate of change?

Back

A function has a constant rate of change if the change in the output (y) is the same for every unit change in the input (x). This is characteristic of linear functions.