Function? Linear?

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 graph can be curved or have various shapes, and it does not have a constant rate of change.

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 any vertical line intersects the graph at more than one point, the graph does not represent a function.

Front

What is 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 not a function?

Back

A relation is not a function if at least one input is associated with more than one output.

Front

Example of a linear equation: y = 2x + 3. Is it linear or nonlinear?

Back

Linear.

Front

Example of a nonlinear equation: y = x^2 + 1. Is it linear or nonlinear?

Back

Nonlinear.

Front

What does the slope of a linear function represent?

Back

The slope represents the rate of change of the function; it indicates how much y changes for a unit change in x.

Front

What is the y-intercept in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented by the value of b in the equation f(x) = mx + b.

Front

Identify if the following relation is a function: {(1,2), (2,3), (1,4)}.

Back

Not a Function (1 is associated with both 2 and 4).