Linear vs. Nonlinear Functions Day 3

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has a constant rate of change and can be expressed in 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. It has a variable rate of change and can include curves, parabolas, and other shapes.

Front

What is the vertical line test?

Back

The vertical line test is a method used to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, then the graph does not represent a function.

Front

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

Back

A table represents a linear function if the differences between consecutive y-values divided by the differences between consecutive x-values are constant.

Front

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

Back

If a relation is not a function, it means that there are at least two different inputs (x-values) that produce the same output (y-value), violating the definition of a function.

Front

Give an example of a linear function.

Back

An example of a linear function is f(x) = 2x + 3, which represents a straight line with 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, which represents a parabola that opens upwards.

Front

What is the slope of a linear function?

Back

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

Front

What is the y-intercept of a linear function?

Back

The y-intercept of a linear function is the point where the graph intersects the y-axis, represented by the value of b in the equation y = mx + b.

Front

What does it mean for a graph to be increasing?

Back

A graph is increasing if, as the x-values increase, the y-values also increase, indicating a positive slope.