Domain/Range and Linear/Non-Linear Functions

Front

What is the definition of a linear function?

Back

A linear function is a function that can be graphically represented in the Cartesian plane 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 the definition of a non-linear function?

Back

A non-linear function is a function that does not create a straight line when graphed. Its graph can be a curve, a circle, or any other shape that is not a straight line.

Front

What are the domain and range of a function?

Back

The domain of a function is the set of all possible input values (x-values), while the range is the set of all possible output values (y-values) that the function can produce.

Front

How do you determine the range of a set of ordered pairs?

Back

To determine the range, list all the second elements (y-values) of the ordered pairs and remove duplicates.

Front

What is the domain of the function represented by the ordered pairs {(1,3), (5,15), (2,6), (4,12), (3,9)}?

Back

The domain is {1, 2, 3, 4, 5}.

Front

What does it mean for a function to be 'not a function'?

Back

A relation is not a function if at least one input (x-value) corresponds to more than one output (y-value).

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of how steep the line is, calculated as the change in y divided by the change in x (rise/run).

Front

What is a 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, it is not a function.

Front

What is the y-intercept of 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

How can you identify a linear function from a table of values?

Back

A function is linear if the differences between consecutive y-values are constant when the x-values increase by the same amount.