Functions

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

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.

Front

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

Back

If the differences between consecutive outputs (y-values) are constant for equal intervals of inputs (x-values), the function is linear.

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of how steep the line is, calculated as the change in y divided by the change in x (rise/run).

Front

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

Back

The y-intercept is the point where the line crosses the y-axis, representing the output value when the input (x) is zero.

Front

If f(x) = 2x + 3, what is f(4)?

Back

f(4) = 2(4) + 3 = 8 + 3 = 11.

Front

What is the independent variable in a function?

Back

The independent variable is the input value of the function, often represented as x.

Front

What is the dependent variable in a function?

Back

The dependent variable is the output value of the function, often represented as y, which depends on the input value.

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.