Linear and Nonlinear 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 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 create a straight line when graphed. Examples include quadratic functions, exponential functions, and trigonometric functions.

Front

What is the slope in the equation y = 3x + 2?

Back

The slope is 3.

Front

What is the y-intercept in the equation y = 3x + 2?

Back

The y-intercept is 2.

Front

How can you determine if a relation is a function?

Back

A relation is a function if every input (x-value) has exactly one output (y-value). This can be checked using the vertical line test on a graph.

Front

What does the term 'rate of change' refer to in a linear function?

Back

The rate of change refers to the slope of the line, indicating how much y changes for a unit change in x.

Front

What is the initial value in the equation y = 5x + 10?

Back

The initial value is 10.

Front

Is the relation {(1,2), (2,3), (1,4)} a function?

Back

No, because the input 1 has two different outputs (2 and 4).

Front

What is the equation of a line with a slope of 4 and a y-intercept of -1?

Back

The equation is y = 4x - 1.

Front

What does it mean if a function is increasing?

Back

A function is increasing if, as x increases, y also increases.