Relations, Functions, & Linear vs. Nonlinear

Front

What is a function?

Back

A function is a relation where each input (x-value) has exactly one output (y-value).

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 a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has 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. Examples include quadratic functions, exponential functions, and trigonometric functions.

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 y-values. If the differences in y-values divided by the differences in x-values are constant, it is linear.

Front

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

Back

A nonlinear function will show varying rates of change between the x-values and y-values. If the differences in y-values divided by the differences in x-values are not constant, it is nonlinear.

Front

What is the slope of a line?

Back

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

Front

What does the y-intercept represent in a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is 0.

Front

What is a relation in mathematics?

Back

A relation is a set of ordered pairs, where each pair consists of an input (x) and an output (y).

Front

Can a relation be a function if it has repeated x-values?

Back

No, a relation cannot be a function if it has repeated x-values with different y-values, as this violates the definition of a function.