Linear Functions, Non-Linear Functions, and Not a Function

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 y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a non-linear function?

Back

A non-linear function is a function that does not create a straight line when graphed. It can include quadratic, exponential, and other types of equations.

Front

What does the term 'not a function' mean?

Back

A relation is 'not a function' if there are two or more outputs for a single input. For example, the relation {(1, 2), (1, 3)} is not a function.

Front

What is the slope in the equation y = mx + b?

Back

The slope (m) represents the rate of change of y with respect to x. It indicates how steep the line is.

Front

What does the y-intercept represent in the equation y = mx + b?

Back

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

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 constant, it is linear.

Front

What is the equation of a line with a slope of 2 and a y-intercept of 3?

Back

The equation is y = 2x + 3.

Front

Which of the following is a linear equation: y = 2x + 5 or y = x^2 + 3?

Back

y = 2x + 5 is a linear equation; y = x^2 + 3 is a non-linear equation.

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.

Front

How do you determine if a set of ordered pairs represents a linear function?

Back

Check if the change in y divided by the change in x is constant for all pairs.