Identifying Linear Functions

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 non-linear function?

Back

A non-linear function is a function that does not form a straight line when graphed. Its rate of change is not constant.

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input. No input can have more than one output.

Front

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

Back

A relation is not a function if at least one input corresponds to multiple outputs.

Front

What is the vertical line test?

Back

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

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/run).

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the graph of a function crosses the y-axis, represented as (0, b) in the function f(x) = mx + b.

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 corresponding y-values.

Front

What is an example of a linear function?

Back

An example of a linear function is f(x) = 2x + 3.

Front

What is an example of a non-linear function?

Back

An example of a non-linear function is f(x) = x^2.