linear and non linear functions

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. In other words, no input value can be paired with more than one output value.

Front

What is the difference between linear and nonlinear functions?

Back

Linear functions create straight-line graphs and have a constant rate of change, while nonlinear functions create curves and do not have a constant rate of change.

Front

What does the term 'y-intercept' mean?

Back

The y-intercept is the point where a graph crosses the y-axis, indicating the value of y when x is 0.

Front

How can you determine if a mapping diagram represents a function?

Back

A mapping diagram represents a function if each input value is connected to exactly one output value.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as the input values increase, the output values also increase.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as the input values increase, the output values decrease.

Front

What is a slope?

Back

The slope of a line measures the steepness and direction of the line, calculated as the change in y divided by the change in x (rise/run).

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not create a straight line when graphed, often involving exponents, roots, or other non-linear operations.

Front

What is a table of values in relation to functions?

Back

A table of values lists pairs of input and output values, showing how each input corresponds to an output.