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. Its rate of change is not constant, and it can be represented by equations that include exponents, roots, or other non-linear terms.

Front

How can you identify a linear function from a graph?

Back

A linear function can be identified from a graph if the points form a straight line. The slope between any two points on the line remains constant.

Front

How can you identify a nonlinear function from a graph?

Back

A nonlinear function can be identified from a graph if the points do not form a straight line. The slope between points changes, indicating a variable rate of change.

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input. In other words, for every x-value, there is one and only one corresponding y-value.

Front

What is the vertical line test?

Back

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

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as the x-values increase, the y-values also increase. This means the graph moves upward from left to right.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as the x-values increase, the y-values decrease. This means the graph moves downward from left to right.

Front

What is a slope in 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). It indicates how much y changes for a unit change in x.

Front

What is a y-intercept?

Back

The y-intercept is the point where the graph of a function crosses the y-axis. It occurs when x = 0.