Alg 1A - Linear vs. Nonlinear Functions

Front

What is a linear function?

Back

A linear function is a function that can be represented by a straight line on a graph. It has the form y = 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 be represented by equations such as quadratics (y = ax^2) or cubics (y = ax^3).

Front

What does it mean for a relation to be a function?

Back

A relation is a function if every input (x-value) has exactly one output (y-value).

Front

How can you identify a linear function from a graph?

Back

A linear function will graph as a straight line, and it will have a constant slope.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise (change in y) over the run (change in x).

Front

What is the y-intercept?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

What is the difference between a linear equation and a nonlinear equation?

Back

A linear equation can be written in the form y = mx + b, while a nonlinear equation cannot be expressed in this form and may include exponents, roots, or other operations that create curves.

Front

How can you tell if a table of values represents a linear function?

Back

If the differences between consecutive y-values are constant for equal differences in x-values, the table represents a linear function.

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is y = x^2, which represents a parabola.

Front

What does it mean if a graph is not a function?

Back

A graph is not a function if any vertical line drawn through the graph intersects it at more than one point.